diff --git a/src/openmc_mcnp_adapter/openmc_conversion.py b/src/openmc_mcnp_adapter/openmc_conversion.py
index 5dc341b..d8648ff 100644
--- a/src/openmc_mcnp_adapter/openmc_conversion.py
+++ b/src/openmc_mcnp_adapter/openmc_conversion.py
@@ -382,8 +382,14 @@ def flip_sense(surf):
             raise NotImplementedError('Surface type "{}" not supported'
                                       .format(s['mnemonic']))
 
-        if s['reflective']:
+        # Set boundary conditions
+        boundary = s.get('boundary')
+        if boundary == 'reflective':
             surf.boundary_type = 'reflective'
+        elif boundary == 'white':
+            surf.boundary_type = 'white'
+        elif boundary == 'periodic':
+            surf.boundary_type = 'periodic'
 
         if 'tr' in s:
             tr_num = s['tr']
@@ -400,6 +406,12 @@ def flip_sense(surf):
         if isinstance(surf, surface_composite.CompositeSurface):
             openmc_surfaces.update((-surf).get_surfaces())
 
+    # Make another pass to set periodic surfaces
+    for s in surfaces:
+        periodic_surface_id = s.get('periodic_surface')
+        if periodic_surface_id is not None:
+            surf.periodic_surface = openmc_surfaces[periodic_surface_id]
+
     return openmc_surfaces
 
 
diff --git a/src/openmc_mcnp_adapter/parse.py b/src/openmc_mcnp_adapter/parse.py
index 05b8561..9249983 100644
--- a/src/openmc_mcnp_adapter/parse.py
+++ b/src/openmc_mcnp_adapter/parse.py
@@ -38,7 +38,7 @@
 _CELL1_RE = re.compile(r'\s*(\d+)\s+(\d+)([ \t0-9:#().dDeE\+-]+)\s*(.*)')
 _CELL2_RE = re.compile(r'\s*(\d+)\s+like\s+(\d+)\s+but\s*(.*)')
 _CELL_FILL_RE = re.compile(r'\s*(\d+)\s*(?:\((.*)\))?')
-_SURFACE_RE = re.compile(r'\s*(\*?\d+)(\s*[-0-9]+)?\s+(\S+)((?:\s+\S+)+)')
+_SURFACE_RE = re.compile(r'\s*([*+]?\d+)(\s*[-0-9]+)?\s+(\S+)((?:\s+\S+)+)')
 _MATERIAL_RE = re.compile(r'\s*[Mm](\d+)((?:\s+\S+)+)')
 _TR_RE = re.compile(r'\s*(\*)?[Tt][Rr](\d+)\s+(.*)')
 _SAB_RE = re.compile(r'\s*[Mm][Tt](\d+)((?:\s+\S+)+)')
@@ -199,10 +199,12 @@ def parse_surface(line):
     g = m.groups()
     surface = {}
     if '*' in g[0]:
-        surface['reflective'] = True
+        surface['boundary'] = 'reflective'
+        uid = int(g[0][1:])
+    elif '+' in g[0]:
+        surface['boundary'] = 'white'
         uid = int(g[0][1:])
     else:
-        surface['reflective'] = False
         uid = int(g[0])
     surface.update({
         'id': uid,
@@ -211,9 +213,8 @@ def parse_surface(line):
     })
     if g[1] is not None:
         if int(g[1]) < 0:
-            surface['periodic'] = int(g[1])
-            # TODO: Move into OpenMC conversion
-            raise NotImplementedError('Periodic boundary conditions not supported')
+            surface['boundary'] = 'periodic'
+            surface['periodic_surface'] = abs(int(g[1]))
         else:
             surface['tr'] = int(g[1])
     return surface
diff --git a/tests/test_geometry.py b/tests/test_geometry.py
index 51d07c8..b67a2f6 100644
--- a/tests/test_geometry.py
+++ b/tests/test_geometry.py
@@ -161,6 +161,7 @@ def test_trcl_macrobody():
         "*FILL=10(2.0 0.0 0.0 0.0 90.0 90.0 90.0 0.0 90.0 90.0 90.0 0.0)",
         "FILL=10(1)",
         "FILL=10(2)",
+        "FILL=10(3)",
     ]
 )
 def test_fill_transformation(keywords):
@@ -176,6 +177,7 @@ def test_fill_transformation(keywords):
     m1     1001.80c  1.0
     tr1    2.0 0.0 0.0 1.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 1.0
     *tr2   2.0 0.0 0.0 0.0 90.0 90.0 90.0 0.0 90.0 90.0 90.0 0.0
+    tr3    2.0 0.0 0.0
     """)
     model = mcnp_str_to_model(mcnp_str)
     geometry = model.geometry
diff --git a/tests/test_surfaces.py b/tests/test_surfaces.py
index 41a9b59..727c054 100644
--- a/tests/test_surfaces.py
+++ b/tests/test_surfaces.py
@@ -30,18 +30,45 @@ def convert_surface(mnemonic: str, params: Sequence[float]) -> openmc.Surface:
     return surfaces[1]
 
 
-def test_reflective_surface():
-    mcnp_str = dedent("""
+@mark.parametrize(
+    "prefix, boundary_type",
+    [
+        ("*", "reflective"),
+        ("+", "white"),
+    ]
+)
+def test_boundary_conditions(prefix, boundary_type):
+    mcnp_str = dedent(f"""
     title
-    1  1.0 -1
+    1  1 1.0 -1
 
-    *1  so 2.0
+    {prefix}1  so 2.0
 
     m1   1001.80c  1.0
     """)
     model = mcnp_str_to_model(mcnp_str)
     surf = model.geometry.get_all_surfaces()[1]
-    assert surf.boundary_type == 'reflective'
+    assert surf.boundary_type == boundary_type
+
+
+def test_boundary_periodic():
+    mcnp_str = dedent("""
+    title
+    1  1  1.0 1 -2 imp:n=1
+    2  0     -1:2  imp:n=0
+
+    1 -2  pz -10.0
+    2 -1  pz  10.0
+
+    m1   1001.80c  1.0
+    """)
+    model = mcnp_str_to_model(mcnp_str)
+    surf1 = model.geometry.get_all_surfaces()[1]
+    surf2 = model.geometry.get_all_surfaces()[2]
+    assert surf1.boundary_type == 'periodic'
+    assert surf1.periodic_surface == surf2
+    assert surf2.boundary_type == 'periodic'
+    assert surf2.periodic_surface == surf1
 
 
 @mark.parametrize(