diff --git a/torchdynamo/allowed_functions.py b/torchdynamo/allowed_functions.py
index 7b17461b03..ffc04f8885 100644
--- a/torchdynamo/allowed_functions.py
+++ b/torchdynamo/allowed_functions.py
@@ -116,7 +116,12 @@ def _allowed_function_ids():
 
     def _is_allowed_module_prefix(obj):
         allowed_modules = ("torch", "math")
-        disallowed_modules = "torch.optim."
+        # torch.nn.modules.rnn is disallowed because these modules internally
+        # flatten their parameters.  This flattening process will call
+        # Tensor.set_ with a Storage, and Storages cannot be traced with
+        # AOTAutograd; so we need to graph-break. To ensure this, we inline
+        # these functions, rather than keep them opaque-ly in the graph.
+        disallowed_modules = ("torch.optim.", "torch.nn.modules.rnn.")
         allowed_modules_dot = tuple([x + "." for x in allowed_modules])
         module = inspect.getmodule(obj)
         if module is None:
@@ -124,7 +129,7 @@ def _is_allowed_module_prefix(obj):
 
         mod_name = module.__name__
 
-        if mod_name.startswith(disallowed_modules):
+        if any(mod_name.startswith(m) for m in disallowed_modules):
             return False
 
         return mod_name in allowed_modules or mod_name.startswith(allowed_modules_dot)