diff --git a/pytorch3d/structures/meshes.py b/pytorch3d/structures/meshes.py
index dffcb3c5..08f804a2 100644
--- a/pytorch3d/structures/meshes.py
+++ b/pytorch3d/structures/meshes.py
@@ -207,7 +207,14 @@ class Meshes(object):
         "equisized",
     ]
 
-    def __init__(self, verts=None, faces=None, textures=None):
+    def __init__(
+        self,
+        verts=None,
+        faces=None,
+        textures=None,
+        *,
+        verts_normals=None,
+    ):
         """
         Args:
             verts:
@@ -229,6 +236,17 @@ class Meshes(object):
                   the same number of faces.
             textures: Optional instance of the Textures class with mesh
                 texture properties.
+            verts_normals:
+                Optional. Can be either
+
+                - List where each element is a tensor of shape (num_verts, 3)
+                  containing the normals of each vertex.
+                - Padded float tensor with shape (num_meshes, max_num_verts, 3).
+                  They should be padded with fill value of 0 so they all have
+                  the same number of vertices.
+                Note that modifying the mesh later, e.g. with offset_verts_,
+                can cause these normals to be forgotten and normals to be recalculated
+                based on the new vertex positions.
 
         Refer to comments above for descriptions of List and Padded representations.
         """
@@ -354,8 +372,8 @@ class Meshes(object):
                     self.equisized = True
 
         elif torch.is_tensor(verts) and torch.is_tensor(faces):
-            if verts.size(2) != 3 and faces.size(2) != 3:
-                raise ValueError("Verts and Faces tensors have incorrect dimensions.")
+            if verts.size(2) != 3 or faces.size(2) != 3:
+                raise ValueError("Verts or Faces tensors have incorrect dimensions.")
             self._verts_padded = verts
             self._faces_padded = faces.to(torch.int64)
             self._N = self._verts_padded.shape[0]
@@ -412,6 +430,36 @@ class Meshes(object):
             self.textures._N = self._N
             self.textures.valid = self.valid
 
+        if verts_normals is not None:
+            self._set_verts_normals(verts_normals)
+
+    def _set_verts_normals(self, verts_normals) -> None:
+        if isinstance(verts_normals, list):
+            if len(verts_normals) != self._N:
+                raise ValueError("Invalid verts_normals input")
+
+            for item, n_verts in zip(verts_normals, self._num_verts_per_mesh):
+                if (
+                    not isinstance(item, torch.Tensor)
+                    or item.ndim != 2
+                    or item.shape[1] != 3
+                    or item.shape[0] != n_verts
+                ):
+                    raise ValueError("Invalid verts_normals input")
+            self._verts_normals_packed = torch.cat(verts_normals, 0)
+        elif torch.is_tensor(verts_normals):
+            if (
+                verts_normals.ndim != 3
+                or verts_normals.size(2) != 3
+                or verts_normals.size(0) != self._N
+            ):
+                raise ValueError("Vertex normals tensor has incorrect dimensions.")
+            self._verts_normals_packed = struct_utils.padded_to_packed(
+                verts_normals, split_size=self._num_verts_per_mesh.tolist()
+            )
+        else:
+            raise ValueError("verts_normals must be a list or tensor")
+
     def __len__(self):
         return self._N
 
@@ -1253,6 +1301,7 @@ class Meshes(object):
     def offset_verts_(self, vert_offsets_packed):
         """
         Add an offset to the vertices of this Meshes. In place operation.
+        If normals are present they may be recalculated.
 
         Args:
             vert_offsets_packed: A Tensor of shape (3,) or the same shape as
@@ -1286,7 +1335,7 @@ class Meshes(object):
                     self._verts_padded[i, : verts.shape[0], :] = verts
 
         # update face areas and normals and vertex normals
-        # only if the original attributes are computed
+        # only if the original attributes are present
         if update_normals and any(
             v is not None
             for v in [self._faces_areas_packed, self._faces_normals_packed]
diff --git a/tests/test_mesh_normal_consistency.py b/tests/test_mesh_normal_consistency.py
index d597facd..3f2f1a93 100644
--- a/tests/test_mesh_normal_consistency.py
+++ b/tests/test_mesh_normal_consistency.py
@@ -223,7 +223,7 @@ class TestMeshNormalConsistency(unittest.TestCase):
         Test Mesh Normal Consistency for a mesh known to have no
         intersecting faces.
         """
-        verts = torch.rand(1, 6, 2)
+        verts = torch.rand(1, 6, 3)
         faces = torch.arange(6).reshape(1, 2, 3)
         meshes = Meshes(verts=verts, faces=faces)
         out = mesh_normal_consistency(meshes)
diff --git a/tests/test_meshes.py b/tests/test_meshes.py
index 7dc7a15c..deee594f 100644
--- a/tests/test_meshes.py
+++ b/tests/test_meshes.py
@@ -1138,6 +1138,20 @@ class TestMeshes(TestCaseMixin, unittest.TestCase):
         self.assertEqual(meshes.faces_normals_padded().shape[0], 0)
         self.assertEqual(meshes.faces_normals_list(), [])
 
+    def test_assigned_normals(self):
+        verts = torch.rand(2, 6, 3)
+        faces = torch.randint(6, size=(2, 4, 3))
+
+        for verts_normals in [list(verts.unbind(0)), verts]:
+            yes_normals = Meshes(
+                verts=verts.clone(), faces=faces, verts_normals=verts_normals
+            )
+            self.assertClose(yes_normals.verts_normals_padded(), verts)
+            yes_normals.offset_verts_(torch.FloatTensor([1, 2, 3]))
+            self.assertClose(yes_normals.verts_normals_padded(), verts)
+            yes_normals.offset_verts_(torch.FloatTensor([1, 2, 3]).expand(12, 3))
+            self.assertFalse(torch.allclose(yes_normals.verts_normals_padded(), verts))
+
     def test_compute_faces_areas_cpu_cuda(self):
         num_meshes = 10
         max_v = 100