diff --git a/crates/uv-pep440/src/version.rs b/crates/uv-pep440/src/version.rs
index 223701692..44db1d88d 100644
--- a/crates/uv-pep440/src/version.rs
+++ b/crates/uv-pep440/src/version.rs
@@ -292,7 +292,7 @@ impl Version {
     ///
     /// When the iterator yields no elements.
     #[inline]
-    pub fn new<I, R>(release_numbers: I) -> Self
+    pub fn new<I, R>(release_segments: I) -> Self
     where
         I: IntoIterator<Item = R>,
         R: Borrow<u64>,
@@ -302,7 +302,7 @@ impl Version {
                 small: VersionSmall::new(),
             },
         }
-        .with_release(release_numbers)
+        .with_release(release_segments)
     }
 
     /// Whether this is an alpha/beta/rc or dev version
diff --git a/crates/uv-pep508/src/marker/algebra.rs b/crates/uv-pep508/src/marker/algebra.rs
index 6b166dbc6..611063aaa 100644
--- a/crates/uv-pep508/src/marker/algebra.rs
+++ b/crates/uv-pep508/src/marker/algebra.rs
@@ -47,6 +47,7 @@
 
 use std::cmp::Ordering;
 use std::fmt;
+use std::hash::Hash;
 use std::ops::Bound;
 use std::sync::{LazyLock, Mutex, MutexGuard};
 
@@ -183,6 +184,55 @@ impl InternerGuard<'_> {
                     }
                 }
             },
+            // `<version key> ~= python_version` and `<version key> ~= python_full_version`
+            MarkerExpression::VersionInvertedTilde { key, specifier } => match key {
+                MarkerValueVersion::ImplementationVersion => {
+                    // The number of segments in the implementation version is unknown and may
+                    // only be a single one not support with tilde equal
+                    return NodeId::FALSE;
+                }
+                MarkerValueVersion::PythonFullVersion => {
+                    // Given `3.10 ~= python_full_version`,
+                    // which matches for 3.10.0, 3.10.1, ... it becomes
+                    // `python_full_version < 3.11 and python_version >= 3.10`
+                    let major = specifier.version().release().first().copied().unwrap_or(0);
+                    let minor = specifier.version().release().get(1).copied().unwrap_or(0);
+
+                    let upper_bound =
+                        VersionSpecifier::less_than_version(Version::new([major, minor + 1, 0]));
+                    let lower_bound = if minor == 0 {
+                        VersionSpecifier::greater_than_equal_version(Version::new([major]))
+                    } else {
+                        VersionSpecifier::greater_than_equal_version(Version::new([major, minor]))
+                    };
+                    let ranges = release_specifier_to_range(upper_bound, true)
+                        .intersection(&release_specifier_to_range(lower_bound, true));
+                    (
+                        Variable::Version(CanonicalMarkerValueVersion::PythonFullVersion),
+                        Edges::from_version_ranges(&ranges),
+                    )
+                }
+                // Normalize `python_version` markers to `python_full_version` nodes.
+                MarkerValueVersion::PythonVersion => {
+                    // Given `3.10 ~= python_version`,
+                    // which matches for 3.0, 3.1, ..., 3.9, 3.10, it becomes
+                    // `python_full_version < 3.11 and python_version >= 3`
+                    let major = specifier.version().release().first().copied().unwrap_or(0);
+                    let minor = specifier.version().release().get(1).copied().unwrap_or(0);
+
+                    let upper_bound =
+                        VersionSpecifier::less_than_version(Version::new([major, minor + 1]));
+                    let lower_bound =
+                        VersionSpecifier::greater_than_equal_version(Version::new([major]));
+                    let ranges = release_specifier_to_range(upper_bound, true)
+                        .intersection(&release_specifier_to_range(lower_bound, true));
+
+                    (
+                        Variable::Version(CanonicalMarkerValueVersion::PythonFullVersion),
+                        Edges::from_version_ranges(&ranges),
+                    )
+                }
+            },
             // A variable representing the output of a version key. Edges correspond
             // to disjoint version ranges.
             MarkerExpression::VersionIn {
@@ -707,7 +757,7 @@ impl InternerGuard<'_> {
         if matches!(i, NodeId::TRUE) {
             let var = Variable::Version(CanonicalMarkerValueVersion::PythonFullVersion);
             let edges = Edges::Version {
-                edges: Edges::from_range(&py_range),
+                edges: Edges::from_ranges(&py_range),
             };
             return self.create_node(var, edges).negate(i);
         }
@@ -1220,7 +1270,7 @@ impl Edges {
         };
 
         Edges::String {
-            edges: Edges::from_range(&range),
+            edges: Edges::from_ranges(&range),
         }
     }
 
@@ -1228,7 +1278,13 @@ impl Edges {
     fn from_specifier(specifier: VersionSpecifier) -> Edges {
         let specifier = release_specifier_to_range(specifier.only_release(), true);
         Edges::Version {
-            edges: Edges::from_range(&specifier),
+            edges: Edges::from_ranges(&specifier),
+        }
+    }
+
+    fn from_version_ranges(ranges: &Ranges<Version>) -> Edges {
+        Edges::Version {
+            edges: Edges::from_ranges(ranges),
         }
     }
 
@@ -1254,7 +1310,7 @@ impl Edges {
         }
 
         Ok(Edges::Version {
-            edges: Edges::from_range(&range),
+            edges: Edges::from_ranges(&range),
         })
     }
 
@@ -1275,25 +1331,25 @@ impl Edges {
         }
 
         Edges::Version {
-            edges: Edges::from_range(&range),
+            edges: Edges::from_ranges(&range),
         }
     }
 
     /// Returns an [`Edges`] where values in the given range are `true`.
-    fn from_range<T>(range: &Ranges<T>) -> SmallVec<(Ranges<T>, NodeId)>
+    fn from_ranges<T>(ranges: &Ranges<T>) -> SmallVec<(Ranges<T>, NodeId)>
     where
         T: Ord + Clone,
     {
         let mut edges = SmallVec::new();
 
         // Add the `true` edges.
-        for (start, end) in range.iter() {
+        for (start, end) in ranges.iter() {
             let range = Ranges::from_range_bounds((start.clone(), end.clone()));
             edges.push((range, NodeId::TRUE));
         }
 
         // Add the `false` edges.
-        for (start, end) in range.complement().iter() {
+        for (start, end) in ranges.complement().iter() {
             let range = Ranges::from_range_bounds((start.clone(), end.clone()));
             edges.push((range, NodeId::FALSE));
         }
@@ -1610,10 +1666,10 @@ fn python_version_to_full_version(specifier: VersionSpecifier) -> Result<Version
     // result in a `python_version` marker of `3.7`. For this reason, we must consider the range
     // of values that would satisfy a `python_version` specifier when truncated in order to transform
     // the specifier into its `python_full_version` equivalent.
-    if let Some((major, minor)) = major_minor {
+    let specifier = if let Some((major, minor)) = major_minor {
         let version = Version::new([major, minor]);
 
-        Ok(match specifier.operator() {
+        match specifier.operator() {
             // `python_version == 3.7` is equivalent to `python_full_version == 3.7.*`.
             Operator::Equal | Operator::ExactEqual => {
                 VersionSpecifier::equals_star_version(version)
@@ -1638,13 +1694,13 @@ fn python_version_to_full_version(specifier: VersionSpecifier) -> Result<Version
                 // Handled above.
                 unreachable!()
             }
-        })
+        }
     } else {
         let [major, minor, ..] = *specifier.version().release() else {
             unreachable!()
         };
 
-        Ok(match specifier.operator() {
+        match specifier.operator() {
             // `python_version` cannot have more than two release segments, and we know
             // that the following release segments aren't purely zeroes so equality is impossible.
             Operator::Equal | Operator::ExactEqual => {
@@ -1668,8 +1724,10 @@ fn python_version_to_full_version(specifier: VersionSpecifier) -> Result<Version
                 // Handled above.
                 unreachable!()
             }
-        })
-    }
+        }
+    };
+
+    Ok(specifier)
 }
 
 /// Compares the start of two ranges that are known to be disjoint.
diff --git a/crates/uv-pep508/src/marker/parse.rs b/crates/uv-pep508/src/marker/parse.rs
index 8e4a39078..ef99ba0c3 100644
--- a/crates/uv-pep508/src/marker/parse.rs
+++ b/crates/uv-pep508/src/marker/parse.rs
@@ -1,7 +1,7 @@
 use arcstr::ArcStr;
 use std::str::FromStr;
 use uv_normalize::{ExtraName, GroupName};
-use uv_pep440::{Version, VersionPattern, VersionSpecifier};
+use uv_pep440::{Operator, Version, VersionPattern, VersionSpecifier};
 
 use crate::cursor::Cursor;
 use crate::marker::MarkerValueExtra;
@@ -282,12 +282,26 @@ pub(crate) fn parse_marker_key_op_value<T: Pep508Url>(
                     parse_inverted_version_expr(&l_string, operator, key, reporter)
                 }
                 // '...' == <env key>
-                MarkerValue::MarkerEnvString(key) => Some(MarkerExpression::String {
-                    key,
+                MarkerValue::MarkerEnvString(key) => {
                     // Invert the operator to normalize the expression order.
-                    operator: operator.invert(),
-                    value: l_string,
-                }),
+                    if let Some(operator) = operator.invert() {
+                        Some(MarkerExpression::String {
+                            key,
+                            operator,
+                            value: l_string,
+                        })
+                    } else {
+                        debug_assert_eq!(operator, MarkerOperator::TildeEqual);
+                        reporter.report(
+                            MarkerWarningKind::StringStringComparison,
+                            format!(
+                                "Comparing a string with `~=` doesn't make sense:
+                                '{l_string}' {operator} {r_value}, will be ignored"
+                            ),
+                        );
+                        None
+                    }
+                }
                 // `"test" in extras` or `"dev" in dependency_groups`
                 MarkerValue::MarkerEnvList(key) => {
                     let operator =
@@ -484,9 +498,6 @@ fn parse_inverted_version_expr(
     key: MarkerValueVersion,
     reporter: &mut impl Reporter,
 ) -> Option<MarkerExpression> {
-    // Invert the operator to normalize the expression order.
-    let marker_operator = marker_operator.invert();
-
     // Not star allowed here, `'3.*' == python_version` is not a valid PEP 440 comparison.
     let version = match value.parse::<Version>() {
         Ok(version) => version,
@@ -503,6 +514,25 @@ fn parse_inverted_version_expr(
         }
     };
 
+    // Invert the operator to normalize the expression order.
+    let Some(marker_operator) = marker_operator.invert() else {
+        // The only operator that can't be inverted is `~=`.
+        debug_assert_eq!(marker_operator, MarkerOperator::TildeEqual);
+        return Some(MarkerExpression::VersionInvertedTilde {
+            key,
+            specifier: match VersionSpecifier::from_version(Operator::TildeEqual, version) {
+                Ok(specifier) => specifier,
+                Err(err) => {
+                    reporter.report(
+                        MarkerWarningKind::Pep440Error,
+                        format!("Invalid operator/version combination: {err}"),
+                    );
+                    return None;
+                }
+            },
+        });
+    };
+
     let Some(operator) = marker_operator.to_pep440_operator() else {
         reporter.report(
             MarkerWarningKind::Pep440Error,
diff --git a/crates/uv-pep508/src/marker/simplify.rs b/crates/uv-pep508/src/marker/simplify.rs
index b1565835b..9a392c8a1 100644
--- a/crates/uv-pep508/src/marker/simplify.rs
+++ b/crates/uv-pep508/src/marker/simplify.rs
@@ -410,6 +410,10 @@ fn is_negation(left: &MarkerExpression, right: &MarkerExpression) -> bool {
                     .negate()
                     .is_some_and(|negated| negated == *specifier2.operator())
         }
+        MarkerExpression::VersionInvertedTilde { .. } => {
+            // The inversion is not a single expression.
+            false
+        }
         MarkerExpression::VersionIn {
             key,
             versions,
diff --git a/crates/uv-pep508/src/marker/tree.rs b/crates/uv-pep508/src/marker/tree.rs
index f874fd447..cea938d04 100644
--- a/crates/uv-pep508/src/marker/tree.rs
+++ b/crates/uv-pep508/src/marker/tree.rs
@@ -268,20 +268,22 @@ impl MarkerOperator {
     }
 
     /// Inverts this marker operator.
-    pub(crate) fn invert(self) -> MarkerOperator {
-        match self {
+    ///
+    /// `~=` has no inverse.
+    pub(crate) fn invert(self) -> Option<MarkerOperator> {
+        Some(match self {
             Self::LessThan => Self::GreaterThan,
             Self::LessEqual => Self::GreaterEqual,
             Self::GreaterThan => Self::LessThan,
             Self::GreaterEqual => Self::LessEqual,
             Self::Equal => Self::Equal,
             Self::NotEqual => Self::NotEqual,
-            Self::TildeEqual => Self::TildeEqual,
+            Self::TildeEqual => return None,
             Self::In => Self::Contains,
             Self::NotIn => Self::NotContains,
             Self::Contains => Self::In,
             Self::NotContains => Self::NotIn,
-        }
+        })
     }
 
     /// Negates this marker operator.
@@ -513,6 +515,12 @@ pub enum MarkerExpression {
         key: MarkerValueVersion,
         specifier: VersionSpecifier,
     },
+    /// Special case for `<version key> ~= python_version` and
+    /// `<version key> ~= python_full_version`.
+    VersionInvertedTilde {
+        key: MarkerValueVersion,
+        specifier: VersionSpecifier,
+    },
     /// A version in list expression, e.g. `<version key> in <quoted list of PEP 440 versions>`.
     ///
     /// A special case of [`MarkerExpression::String`] with the [`MarkerOperator::In`] operator for
@@ -526,7 +534,7 @@ pub enum MarkerExpression {
         versions: Vec<Version>,
         operator: ContainerOperator,
     },
-    /// An string marker comparison, e.g. `sys_platform == '...'`.
+    /// A string marker comparison, e.g. `sys_platform == '...'`.
     ///
     /// Inverted string expressions, e.g `'...' == sys_platform`, are also normalized to this form.
     String {
@@ -551,6 +559,8 @@ pub enum MarkerExpression {
 pub(crate) enum MarkerExpressionKind {
     /// A version expression, e.g. `<version key> <version op> <quoted PEP 440 version>`.
     Version(MarkerValueVersion),
+    /// An inverted tilde-equal version expression, e.g. `<version key> ~= <quoted PEP 440 version>`.
+    VersionInvertedTilde(MarkerValueVersion),
     /// A version `in` expression, e.g. `<version key> in <quoted list of PEP 440 versions>`.
     VersionIn(MarkerValueVersion),
     /// A string marker comparison, e.g. `sys_platform == '...'`.
@@ -667,6 +677,9 @@ impl MarkerExpression {
     pub(crate) fn kind(&self) -> MarkerExpressionKind {
         match self {
             MarkerExpression::Version { key, .. } => MarkerExpressionKind::Version(*key),
+            MarkerExpression::VersionInvertedTilde { key, .. } => {
+                MarkerExpressionKind::VersionInvertedTilde(*key)
+            }
             MarkerExpression::VersionIn { key, .. } => MarkerExpressionKind::VersionIn(*key),
             MarkerExpression::String { key, .. } => MarkerExpressionKind::String(*key),
             MarkerExpression::List { pair, .. } => MarkerExpressionKind::List(pair.key()),
@@ -686,6 +699,10 @@ impl Display for MarkerExpression {
                 }
                 write!(f, "{key} {op} '{version}'")
             }
+            MarkerExpression::VersionInvertedTilde { key, specifier } => {
+                let (op, version) = (specifier.operator(), specifier.version());
+                write!(f, "'{version}' {op} {key}")
+            }
             MarkerExpression::VersionIn {
                 key,
                 versions,
@@ -703,7 +720,8 @@ impl Display for MarkerExpression {
                     operator,
                     MarkerOperator::Contains | MarkerOperator::NotContains
                 ) {
-                    return write!(f, "'{value}' {} {key}", operator.invert());
+                    // Unwrap safety: `in` and `not in` have inverses.
+                    return write!(f, "'{value}' {} {key}", operator.invert().unwrap());
                 }
 
                 write!(f, "{key} {operator} '{value}'")
@@ -2843,6 +2861,39 @@ mod test {
         );
     }
 
+    #[test]
+    fn test_tilde_equal_inverted_normalization() {
+        assert_eq!(
+            m("'3.0' ~= python_version"),
+            m("python_version >= '3' and python_version <= '3.0'")
+        );
+
+        assert_eq!(
+            m("'3.10' ~= python_version"),
+            m("python_version >= '3' and python_version <= '3.10'")
+        );
+
+        assert_eq!(
+            m("'3.10.0' ~= python_version"),
+            m("python_version >= '3' and python_version <= '3.10'")
+        );
+
+        assert_eq!(
+            m("'3.10' ~= python_full_version"),
+            m("python_full_version < '3.11' and python_full_version >= '3.10.0'")
+        );
+
+        assert_eq!(
+            m("'3.10.10' ~= python_full_version"),
+            m("python_full_version < '3.11' and python_full_version >= '3.10.0'")
+        );
+
+        assert_simplifies(
+            "python_version == '3.0.*'",
+            "python_full_version == '3.0.*'",
+        );
+    }
+
     /// This tests marker implication.
     ///
     /// Specifically, these test cases come from a [bug] where `foo` and `bar`
@@ -2926,7 +2977,7 @@ mod test {
         );
         assert_eq!(
             m("'3.6' ~= python_version").negate(),
-            m("python_version < '3.6' or python_version != '3.*'")
+            m("python_full_version < '3' or python_full_version >= '3.7'")
         );
         assert_eq!(
             m("python_version ~= '3.6.2'").negate(),