diff --git a/onnxscript/ir/_core.py b/onnxscript/ir/_core.py
index 69423a2e1..519221509 100644
--- a/onnxscript/ir/_core.py
+++ b/onnxscript/ir/_core.py
@@ -32,11 +32,13 @@
     Iterator,
     OrderedDict,
     Sequence,
+    SupportsInt,
     Union,
 )
 
 import ml_dtypes
 import numpy as np
+from typing_extensions import TypeIs
 
 import onnxscript
 from onnxscript.ir import (
@@ -859,12 +861,37 @@ def __repr__(self) -> str:
         return f"{self.__class__.__name__}({self._value})"
 
 
+def _is_int_compatible(value: object) -> TypeIs[SupportsInt]:
+    """Return True if the value is int compatible."""
+    if isinstance(value, int):
+        return True
+    if hasattr(value, "__int__"):
+        # For performance reasons, we do not use isinstance(value, SupportsInt)
+        return True
+    return False
+
+
+def _maybe_convert_to_symbolic_dim(
+    dim: int | SupportsInt | SymbolicDim | str | None,
+) -> SymbolicDim | int:
+    """Convert the value to a SymbolicDim if it is not an int."""
+    if dim is None or isinstance(dim, str):
+        return SymbolicDim(dim)
+    if _is_int_compatible(dim):
+        return int(dim)
+    if isinstance(dim, SymbolicDim):
+        return dim
+    raise TypeError(
+        f"Expected int, str, None or SymbolicDim, but value {dim!r} has type '{type(dim)}'"
+    )
+
+
 class Shape(_protocols.ShapeProtocol, _display.PrettyPrintable):
     __slots__ = ("_dims", "_frozen")
 
     def __init__(
         self,
-        dims: Iterable[int | SymbolicDim | str | None],
+        dims: Iterable[int | SupportsInt | SymbolicDim | str | None],
         /,
         denotations: Iterable[str | None] | None = None,
         frozen: bool = False,
@@ -885,8 +912,7 @@ def __init__(
                 is useful when the shape is initialized by a Tensor.
         """
         self._dims: list[int | SymbolicDim] = [
-            SymbolicDim(dim) if not isinstance(dim, (int, SymbolicDim)) else dim
-            for dim in dims
+            _maybe_convert_to_symbolic_dim(dim) for dim in dims
         ]
         self._denotations: list[str | None] = (
             list(denotations) if denotations is not None else [None] * len(self._dims)
@@ -946,12 +972,8 @@ def __setitem__(self, index: int, value: int | SymbolicDim | str | None) -> None
         """
         if self._frozen:
             raise TypeError("The shape is frozen and cannot be modified.")
-        if isinstance(value, str) or value is None:
-            value = SymbolicDim(value)
-        if not isinstance(value, (int, SymbolicDim)):
-            raise TypeError(f"Expected int, str, None or SymbolicDim, got '{type(value)}'")
 
-        self._dims[index] = value
+        self._dims[index] = _maybe_convert_to_symbolic_dim(value)
 
     def get_denotation(self, index: int) -> str | None:
         """Return the denotation of the dimension at the index.
@@ -986,7 +1008,7 @@ def __str__(self) -> str:
     def __eq__(self, other: object) -> bool:
         """Return True if the shapes are equal.
 
-        Two shapes are eqaul if all their dimensions are equal.
+        Two shapes are equal if all their dimensions are equal.
         """
         if isinstance(other, Shape):
             return self._dims == other._dims
@@ -997,6 +1019,33 @@ def __eq__(self, other: object) -> bool:
     def __ne__(self, other: object) -> bool:
         return not self.__eq__(other)
 
+    @typing.overload
+    def is_static(self, dim: int) -> bool:  # noqa: D418
+        """Return True if the dimension is static."""
+
+    @typing.overload
+    def is_static(self) -> bool:  # noqa: D418
+        """Return True if all dimensions are static."""
+
+    def is_static(self, dim=None) -> bool:
+        """Return True if the dimension is static. If dim is None, return True if all dimensions are static."""
+        if dim is None:
+            return all(isinstance(dim, int) for dim in self._dims)
+        return isinstance(self[dim], int)
+
+    @typing.overload
+    def is_dynamic(self, dim: int) -> bool:  # noqa: D418
+        """Return True if the dimension is dynamic."""
+
+    @typing.overload
+    def is_dynamic(self) -> bool:  # noqa: D418
+        """Return True if any dimension is dynamic."""
+
+    def is_dynamic(self, dim=None) -> bool:
+        if dim is None:
+            return not self.is_static()
+        return not self.is_static(dim)
+
 
 def _quoted(string: str) -> str:
     """Return a quoted string.
diff --git a/onnxscript/ir/_core_test.py b/onnxscript/ir/_core_test.py
index 498a8a3ce..8662a8c01 100644
--- a/onnxscript/ir/_core_test.py
+++ b/onnxscript/ir/_core_test.py
@@ -520,6 +520,30 @@ def test_int_dimensions_are_python_ints(self):
         shape = _core.Shape([42])
         self.assertIsInstance(shape[0], int)
 
+    def test_str_dimensions_are_symbolic_dims(self):
+        shape = _core.Shape(["any string"])
+        self.assertIsInstance(shape[0], _core.SymbolicDim)
+
+    def test_none_dimensions_are_symbolic_dims(self):
+        shape = _core.Shape([None])
+        self.assertIsInstance(shape[0], _core.SymbolicDim)
+
+    def test_init_raises_when_dims_is_not_a_list(self):
+        with self.assertRaises(TypeError):
+            _core.Shape(42)
+
+    def test_init_converts_np_shape_to_tuple(self):
+        dims = np.array([42, 42])
+        shape = _core.Shape(dims)
+        self.assertEqual(shape.dims, tuple(dims))
+
+    def test_init_converts_np_int_to_python_int(self):
+        dims = [np.int32(42)]
+        shape = _core.Shape(dims)
+        self.assertIsInstance(shape[0], int)
+        self.assertNotIsInstance(shape[0], np.int32)
+        self.assertIsInstance(shape.dims[0], int)
+
     @parameterized.parameterized.expand(
         [
             ("empty", (), ()),
@@ -623,6 +647,10 @@ def test_setitem(self, _: str, value):
         else:
             self.assertEqual(dim, value)
 
+    def test_len(self):
+        shape = _core.Shape([42, "any string"])
+        self.assertEqual(len(shape), 2)
+
     def test_get_denotation(self):
         shape = _core.Shape([42], denotations=("DATA_CHANNEL",))
         self.assertEqual(shape.get_denotation(0), "DATA_CHANNEL")
@@ -637,6 +665,56 @@ def test_set_denotation_is_still_possible_when_shape_is_frozen(self):
         shape.set_denotation(0, "UPDATED")
         self.assertEqual(shape.get_denotation(0), "UPDATED")
 
+    def test_is_static(self):
+        dim_from_numpy = np.array([42]).shape[0]
+        np_int = np.int32(42)
+        shape = _core.Shape([42, "any string", dim_from_numpy, np_int])
+        self.assertTrue(shape.is_static(0))
+        self.assertFalse(shape.is_static(1))
+        self.assertTrue(shape.is_static(2))
+        self.assertTrue(shape.is_static(3))
+        self.assertFalse(shape.is_static())
+
+    def test_is_static_raises_when_index_out_of_range(self):
+        shape = _core.Shape([42])
+        with self.assertRaises(IndexError):
+            shape.is_static(1)
+
+    def test_is_static_on_whole_shape(self):
+        shape = _core.Shape([42, "any string"])
+        self.assertFalse(shape.is_static())
+        shape = _core.Shape([42, 42])
+        self.assertTrue(shape.is_static())
+
+    def test_is_static_on_empty_shape(self):
+        shape = _core.Shape(())
+        self.assertTrue(shape.is_static())
+
+    def test_is_dynamic(self):
+        dim_from_numpy = np.array([42]).shape[0]
+        np_int = np.int32(42)
+        shape = _core.Shape([42, "any string", dim_from_numpy, np_int])
+        self.assertFalse(shape.is_dynamic(0))
+        self.assertTrue(shape.is_dynamic(1))
+        self.assertFalse(shape.is_dynamic(2))
+        self.assertFalse(shape.is_dynamic(3))
+        self.assertTrue(shape.is_dynamic())
+
+    def test_is_dynamic_raises_when_index_out_of_range(self):
+        shape = _core.Shape([42])
+        with self.assertRaises(IndexError):
+            shape.is_dynamic(1)
+
+    def test_is_dynamic_on_whole_shape(self):
+        shape = _core.Shape([42, "any string"])
+        self.assertTrue(shape.is_dynamic())
+        shape = _core.Shape([42, 42])
+        self.assertFalse(shape.is_dynamic())
+
+    def test_is_dynamic_on_empty_shape(self):
+        shape = _core.Shape(())
+        self.assertFalse(shape.is_dynamic())
+
 
 class ValueTest(unittest.TestCase):
     def test_initialize(self):