diff --git a/crates/uv-pep440/src/version.rs b/crates/uv-pep440/src/version.rs
index 77a33e0d96c3c..488e95c11d1c8 100644
--- a/crates/uv-pep440/src/version.rs
+++ b/crates/uv-pep440/src/version.rs
@@ -2266,7 +2266,19 @@ impl<'a> Parser<'a> {
         if digits.is_empty() {
             return Ok(None);
         }
-        Ok(Some(parse_u64(digits)?))
+        let n = parse_u64(digits)?;
+        // Reject `u64::MAX` to prevent arithmetic overflow in downstream code
+        // that computes `segment + 1` (e.g., `~=` upper bound, `==*` upper
+        // bound, `python_version` marker algebra). This only applies to version
+        // segments (release, epoch, pre/post/dev), not local version segments
+        // which don't undergo arithmetic.
+        if n == u64::MAX {
+            return Err(ErrorKind::NumberTooBig {
+                bytes: digits.to_vec(),
+            }
+            .into());
+        }
+        Ok(Some(n))
     }
 
     /// Turns whatever state has been gathered into a `VersionPattern`.
@@ -2581,7 +2593,7 @@ impl std::fmt::Display for VersionParseError {
                     f,
                     "expected number less than or equal to {}, \
                      but number found in {string:?} exceeds it",
-                    u64::MAX,
+                    u64::MAX - 1,
                 )
             }
             ErrorKind::NoLeadingNumber => {
@@ -4182,6 +4194,7 @@ mod tests {
         assert_eq!(p("10a"), Err(ErrorKind::InvalidDigit { got: b'a' }.into()));
         assert_eq!(p("10["), Err(ErrorKind::InvalidDigit { got: b'[' }.into()));
         assert_eq!(p("10/"), Err(ErrorKind::InvalidDigit { got: b'/' }.into()));
+        // u64::MAX + 1 is rejected (overflow during parsing).
         assert_eq!(
             p("18446744073709551616"),
             Err(ErrorKind::NumberTooBig {
diff --git a/crates/uv-pep440/src/version_ranges.rs b/crates/uv-pep440/src/version_ranges.rs
index 2fc090764eb6d..22f34a8c8587a 100644
--- a/crates/uv-pep440/src/version_ranges.rs
+++ b/crates/uv-pep440/src/version_ranges.rs
@@ -621,4 +621,31 @@ mod tests {
         let v = "0.12.0.post1".parse::<Version>().unwrap();
         assert!(!range.contains(&v), "should exclude 0.12.0.post1");
     }
+
+    /// Do not panic with `u64::MAX` causing an `u64::MAX + 1` overflow.
+    #[test]
+    fn u64_max_version_segments_rejected_at_parse_time() {
+        assert!(
+            "~=18446744073709551615.0"
+                .parse::<VersionSpecifier>()
+                .is_err()
+        );
+        assert!(
+            "==18446744073709551615.*"
+                .parse::<VersionSpecifier>()
+                .is_err()
+        );
+
+        // u64::MAX - 1 is still accepted.
+        assert!(
+            "~=18446744073709551614.0"
+                .parse::<VersionSpecifier>()
+                .is_ok()
+        );
+        assert!(
+            "==18446744073709551614.*"
+                .parse::<VersionSpecifier>()
+                .is_ok()
+        );
+    }
 }
diff --git a/crates/uv-pep440/src/version_specifier.rs b/crates/uv-pep440/src/version_specifier.rs
index 155585fb2cee2..ae1411637affd 100644
--- a/crates/uv-pep440/src/version_specifier.rs
+++ b/crates/uv-pep440/src/version_specifier.rs
@@ -2051,4 +2051,16 @@ Failed to parse version: Unexpected end of version specifier, expected operator.
             "The ~= operator requires at least two segments in the release version"
         );
     }
+
+    /// Do not panic with `u64::MAX` causing an `u64::MAX + 1` overflow.
+    #[test]
+    fn bounding_specifiers_u64_max_rejected_at_parse_time() {
+        assert!(VersionSpecifier::from_str("~=3.18446744073709551615.0").is_err());
+        assert!(VersionSpecifier::from_str("~=18446744073709551615.0").is_err());
+
+        // u64::MAX - 1 is accepted and bounding_specifiers does not overflow.
+        let specifier = VersionSpecifier::from_str("~=3.18446744073709551614.0").unwrap();
+        let tilde = TildeVersionSpecifier::from_specifier(specifier).unwrap();
+        let (_lower, _upper) = tilde.bounding_specifiers();
+    }
 }
diff --git a/crates/uv-pep508/src/marker/algebra.rs b/crates/uv-pep508/src/marker/algebra.rs
index 8a170202ea180..e9a138ff13104 100644
--- a/crates/uv-pep508/src/marker/algebra.rs
+++ b/crates/uv-pep508/src/marker/algebra.rs
@@ -1814,4 +1814,25 @@ mod tests {
         let b = m().and(not_x86, windows);
         assert_eq!(m().or(a, b), windows);
     }
+
+    /// Do not panic with `u64::MAX` causing an `u64::MAX + 1` overflow.
+    #[test]
+    fn python_version_marker_u64_max() {
+        // The parse error is converted to a warning and the condition is ignored.
+        assert_eq!(
+            MarkerExpression::from_str("python_version > '3.18446744073709551615'").unwrap(),
+            None,
+        );
+        assert_eq!(
+            MarkerExpression::from_str("python_version <= '3.18446744073709551615'").unwrap(),
+            None,
+        );
+
+        // `u64::MAX - 1` accepted
+        assert!(
+            MarkerExpression::from_str("python_version > '3.18446744073709551614'")
+                .unwrap()
+                .is_some()
+        );
+    }
 }
diff --git a/crates/uv/tests/it/lock.rs b/crates/uv/tests/it/lock.rs
index c30e8d1c31a26..38b498312209a 100644
--- a/crates/uv/tests/it/lock.rs
+++ b/crates/uv/tests/it/lock.rs
@@ -33368,3 +33368,33 @@ fn lock_check_multiple_default_indexes_explicit_assignment_dependency_group() ->
 
     Ok(())
 }
+
+/// Do not panic with `u64::MAX` causing an `u64::MAX + 1` overflow.
+#[test]
+fn lock_tilde_equal_version_u64_max_rejected() -> Result<()> {
+    let context = uv_test::test_context!("3.12");
+
+    let pyproject_toml = context.temp_dir.child("pyproject.toml");
+    pyproject_toml.write_str(indoc! { r#"
+        [project]
+        name = "foo"
+        version = "0.1.0"
+        requires-python = ">=3.12"
+        dependencies = ["bar~=18446744073709551615.0"]
+    "#})?;
+
+    uv_snapshot!(context.filters(), context.lock(), @r#"
+    success: false
+    exit_code: 1
+    ----- stdout -----
+
+    ----- stderr -----
+      × Failed to build `foo @ file://[TEMP_DIR]/`
+      ├─▶ Failed to parse metadata from built wheel
+      ╰─▶ expected number less than or equal to 18446744073709551614, but number found in "18446744073709551615" exceeds it
+          bar ~=18446744073709551615.0
+              ^^^^^^^^^^^^^^^^^^^^^^^^
+    "#);
+
+    Ok(())
+}