diff --git a/openmc/filter.py b/openmc/filter.py
index 0b4929a8be..6e389ba2d7 100644
--- a/openmc/filter.py
+++ b/openmc/filter.py
@@ -750,7 +750,7 @@ class MeshFilter(Filter):
         cv.check_type('filter mesh', mesh, openmc.MeshBase)
         self._mesh = mesh
         if isinstance(mesh, openmc.UnstructuredMesh):
-            self.bins = []
+            self.bins = [ (n, 1, 1) for n in range(1, mesh.volumes.size + 1) ]
         else:
             self.bins = list(mesh.indices)
 
diff --git a/openmc/mesh.py b/openmc/mesh.py
index 41d6beae4e..8b199fa25f 100644
--- a/openmc/mesh.py
+++ b/openmc/mesh.py
@@ -654,7 +654,8 @@ class UnstructuredMesh(MeshBase):
 
         mesh = cls(mesh_id)
         mesh.filename = group['filename'][()].decode()
-        mesh.volumes = group['volumes'][()]
+        vol_data = group['volumes'][()]
+        mesh.volumes = np.reshape(vol_data, (vol_data.shape[0], 1))
 
         return mesh