diff --git a/crates/ty_python_semantic/resources/mdtest/import/basic.md b/crates/ty_python_semantic/resources/mdtest/import/basic.md
index 8e7538190ef06a..45abcf50185333 100644
--- a/crates/ty_python_semantic/resources/mdtest/import/basic.md
+++ b/crates/ty_python_semantic/resources/mdtest/import/basic.md
@@ -205,3 +205,18 @@ python-version = "3.13"
 import aifc  # error: [unresolved-import]
 from distutils import sysconfig  # error: [unresolved-import]
 ```
+
+## Cannot shadow core standard library modules
+
+`types.py`:
+
+```py
+x: int
+```
+
+```py
+# error: [unresolved-import]
+from types import x
+
+from types import FunctionType
+```
diff --git a/crates/ty_python_semantic/src/module_resolver/resolver.rs b/crates/ty_python_semantic/src/module_resolver/resolver.rs
index af4acc966f44c6..be6f40c2465f2a 100644
--- a/crates/ty_python_semantic/src/module_resolver/resolver.rs
+++ b/crates/ty_python_semantic/src/module_resolver/resolver.rs
@@ -535,14 +535,23 @@ struct ModuleNameIngredient<'db> {
     pub(super) name: ModuleName,
 }
 
+/// Returns `true` if the module name refers to a standard library module which can't be shadowed
+/// by a first-party module.
+///
+/// This includes "builtin" modules, which can never be shadowed at runtime either, as well as the
+/// `types` module, which tends to be imported early in Python startup, so can't be consistently
+/// shadowed, and is important to type checking.
+fn is_non_shadowable(minor_version: u8, module_name: &str) -> bool {
+    module_name == "types" || ruff_python_stdlib::sys::is_builtin_module(minor_version, module_name)
+}
+
 /// Given a module name and a list of search paths in which to lookup modules,
 /// attempt to resolve the module name
 fn resolve_name(db: &dyn Db, name: &ModuleName) -> Option<ResolvedName> {
     let program = Program::get(db);
     let python_version = program.python_version(db);
     let resolver_state = ResolverContext::new(db, python_version);
-    let is_builtin_module =
-        ruff_python_stdlib::sys::is_builtin_module(python_version.minor, name.as_str());
+    let is_non_shadowable = is_non_shadowable(python_version.minor, name.as_str());
 
     let name = RelaxedModuleName::new(name);
     let stub_name = name.to_stub_package();
@@ -553,7 +562,8 @@ fn resolve_name(db: &dyn Db, name: &ModuleName) -> Option<ResolvedName> {
         // the module name always resolves to the stdlib module,
         // even if there's a module of the same name in the first-party root
         // (which would normally result in the stdlib module being overridden).
-        if is_builtin_module && !search_path.is_standard_library() {
+        // TODO: offer a diagnostic if there is a first-party module of the same name
+        if is_non_shadowable && !search_path.is_standard_library() {
             continue;
         }
 
diff --git a/crates/ty_python_semantic/tests/corpus.rs b/crates/ty_python_semantic/tests/corpus.rs
index 971b4cdc79dc49..799e76dd11ab4c 100644
--- a/crates/ty_python_semantic/tests/corpus.rs
+++ b/crates/ty_python_semantic/tests/corpus.rs
@@ -116,13 +116,6 @@ fn run_corpus_tests(pattern: &str) -> anyhow::Result<()> {
             .with_context(|| format!("Failed to read test file: {path}"))?;
 
         let mut check_with_file_name = |path: &SystemPath| {
-            if relative_path.file_name() == Some("types.pyi") {
-                println!(
-                    "Skipping {relative_path:?}: paths with `types.pyi` as their final segment cause a stack overflow"
-                );
-                return;
-            }
-
             db.memory_file_system().write_file_all(path, &code).unwrap();
             File::sync_path(&mut db, path);