diff --git a/openmc/mesh.py b/openmc/mesh.py
index fefc6d707..2fe873d2b 100644
--- a/openmc/mesh.py
+++ b/openmc/mesh.py
@@ -156,7 +156,7 @@ class Mesh(object):
         check_type('type for mesh ID="{0}"'.format(self._id),
                    meshtype, basestring)
         check_value('type for mesh ID="{0}"'.format(self._id),
-                    meshtype, ['regular', 'hexagonal'])
+                    meshtype, ['regular'])
         self._type = meshtype
 
     @dimension.setter
diff --git a/src/constants.F90 b/src/constants.F90
index 962c4a6a2..53891cdaa 100644
--- a/src/constants.F90
+++ b/src/constants.F90
@@ -312,6 +312,10 @@ module constants
        FILTER_ENERGYOUT   = 8, &
        FILTER_DISTRIBCELL = 9
 
+  ! Mesh types
+  integer, parameter :: &
+       MESH_REGULAR = 1
+
   ! Tally surface current directions
   integer, parameter :: &
        IN_RIGHT  = 1,   &
diff --git a/src/input_xml.F90 b/src/input_xml.F90
index e6e644459..3899d43f0 100644
--- a/src/input_xml.F90
+++ b/src/input_xml.F90
@@ -2188,9 +2188,11 @@ contains
            call get_node_value(node_mesh, "type", temp_str)
       select case (to_lower(temp_str))
       case ('rect', 'rectangle', 'rectangular')
-        m % type = LATTICE_RECT
-      case ('hex', 'hexagon', 'hexagonal')
-        m % type = LATTICE_HEX
+        call warning("Mesh type '" // trim(temp_str) // "' is deprecated. &
+             &Please use 'regular' instead.")
+        m % type = MESH_REGULAR
+      case ('regular')
+        m % type = MESH_REGULAR
       case default
         call fatal_error("Invalid mesh type: " // trim(temp_str))
       end select
diff --git a/src/relaxng/tallies.rnc b/src/relaxng/tallies.rnc
index c2e0860b8..ee93d273c 100644
--- a/src/relaxng/tallies.rnc
+++ b/src/relaxng/tallies.rnc
@@ -1,8 +1,8 @@
 element tallies {
   element mesh {
     (element id { xsd:int } | attribute id { xsd:int }) &
-    (element type { ( "rectangular" | "hexagonal" ) } |
-      attribute type { ( "rectangular" | "hexagonal" ) }) &
+    (element type { ( "regular" ) } |
+      attribute type { ( "regular" ) }) &
     (element dimension { list { xsd:positiveInteger+ } } |
       attribute dimension { list { xsd:positiveInteger+ } }) &
     (element lower_left { list { xsd:double+ } } |
@@ -32,7 +32,7 @@ element tallies {
     element nuclides {
       list { xsd:string { maxLength = "12" }+ }
     }? &
-    element scores { 
+    element scores {
       list { xsd:string { maxLength = "20" }+ }
     } &
     element trigger {
diff --git a/src/relaxng/tallies.rng b/src/relaxng/tallies.rng
index 9ea941fea..76973e855 100644
--- a/src/relaxng/tallies.rng
+++ b/src/relaxng/tallies.rng
@@ -14,16 +14,10 @@
           </choice>
           <choice>
             <element name="type">
-              <choice>
-                <value>rectangular</value>
-                <value>hexagonal</value>
-              </choice>
+              <value>regular</value>
             </element>
             <attribute name="type">
-              <choice>
-                <value>rectangular</value>
-                <value>hexagonal</value>
-              </choice>
+              <value>regular</value>
             </attribute>
           </choice>
           <choice>