diff --git a/openmc/model/__init__.py b/openmc/model/__init__.py
index 9fa999dd4..bd43b14ce 100644
--- a/openmc/model/__init__.py
+++ b/openmc/model/__init__.py
@@ -1,3 +1,4 @@
 from .triso import *
 from .model import *
 from .funcs import *
+from .surface_composite import *
diff --git a/openmc/model/surface_composite.py b/openmc/model/surface_composite.py
new file mode 100644
index 000000000..66afd4b1c
--- /dev/null
+++ b/openmc/model/surface_composite.py
@@ -0,0 +1,164 @@
+from copy import copy
+
+import openmc
+
+
+class CompositeMixin:
+    def evaluate(self, point):
+        raise NotImplementedError('Composite surfaces do not have a surface equation.')
+
+    def _get_base_coeffs(self):
+        raise NotImplementedError('Composite surfaces do not have base coefficients.')
+
+    def translate(self, vector, inplace=False):
+        surf = self if inplace else copy(self)
+        for name in self._surface_names:
+            s = getattr(surf, name)
+            setattr(surf, name, s.translate(vector, inplace))
+        return surf
+
+    def rotate(self, rotation):
+        surf = copy(self)
+        for name in self._surface_names:
+            s = getattr(surf, name)
+            setattr(surf, name, s.rotate(rotation))
+        return surf
+
+    def __repr__(self):
+        return "<{} at 0x{:x}>".format(type(self).__name__, id(self))
+
+
+class RightCircularCylinder(CompositeMixin, openmc.Surface):
+    _surface_names = ('cyl', 'bottom', 'top')
+
+    def __init__(self, center_base, height, radius, axis='z',
+                 boundary_type='transmission'):
+        kwargs = {'boundary_type': boundary_type}
+        cx, cy, cz = center_base
+        if axis == 'x':
+            self.cyl = openmc.XCylinder(y0=cy, z0=cz, r=radius, **kwargs)
+            self.bottom = openmc.XPlane(x0=cx, **kwargs)
+            self.top = openmc.XPlane(x0=cx + height, **kwargs)
+        elif axis == 'y':
+            self.cyl = openmc.YCylinder(x0=cx, z0=cz, r=radius, **kwargs)
+            self.bottom = openmc.YPlane(y0=cy, **kwargs)
+            self.top = openmc.YPlane(y0=cy + height, **kwargs)
+        elif axis == 'z':
+            self.cyl = openmc.ZCylinder(x0=cx, y0=cy, r=radius, **kwargs)
+            self.bottom = openmc.ZPlane(z0=cz, **kwargs)
+            self.top = openmc.ZPlane(z0=cz + height, **kwargs)
+
+    def __neg__(self):
+        return -self.cyl & +self.bottom & -self.top
+
+    def __pos__(self):
+        return +self.cyl | -self.bottom | +self.top
+
+
+class RectangularParallelepiped(CompositeMixin, openmc.Surface):
+    _surface_names = ('xmin', 'xmax', 'ymin', 'ymax', 'zmin', 'zmax')
+
+    def __init__(self, xmin, xmax, ymin, ymax, zmin, zmax, boundary_type='transmission'):
+        kwargs = {'boundary_type': boundary_type}
+        self.xmin = openmc.XPlane(x0=xmin, **kwargs)
+        self.xmax = openmc.XPlane(x0=xmax, **kwargs)
+        self.ymin = openmc.YPlane(y0=ymin, **kwargs)
+        self.ymax = openmc.YPlane(y0=ymax, **kwargs)
+        self.zmin = openmc.ZPlane(z0=zmin, **kwargs)
+        self.zmax = openmc.ZPlane(z0=zmax, **kwargs)
+
+    def __neg__(self):
+        return +self.xmin & -self.xmax & +self.ymin & -self.ymax & +self.zmin & -self.zmax
+
+    def __pos__(self):
+        return -self.xmin | +self.ymax | -self.ymin | +self.ymax | -self.zmin | +self.zmax
+
+
+class Box(CompositeMixin, openmc.Surface):
+    _surface_names = ('xmin', 'xmax', 'ymin', 'ymax', 'zmin', 'zmax')
+
+    def __init__(self, v, a1, a2, a3, boundary_type='transmission'):
+        kwargs = {'boundary_type': boundary_type}
+        vx, vy, vz = v
+        a1x, a1y, a1z = a1
+        a2x, a2y, a2z = a2
+        a3x, a3y, a3z = a3
+
+        # Only support boxes with axis-aligned vectors
+        if any(x != 0.0 for x in (a1y, a1z, a2x, a2z, a3x, a3y)):
+            raise NotImplementedError('Box macrobody with non-axis-aligned '
+                                      'vector not supported.')
+
+        # Determine each side of the box
+        if a1x > 0:
+            xmin, xmax = vx, vx + a1x
+        else:
+            xmin, xmax = vx + a1x, vx
+        if a2y > 0:
+            ymin, ymax = vy, vy + a2y
+        else:
+            ymin, ymax = vy + a2y, vy
+        if a3z > 0:
+            zmin, zmax = vz, vz + a3z
+        else:
+            zmin, zmax = vz + a3z, vz
+
+        # Create surfaces
+        self.xmin = openmc.XPlane(x0=xmin, **kwargs)
+        self.xmax = openmc.XPlane(x0=xmax, **kwargs)
+        self.ymin = openmc.YPlane(y0=ymin, **kwargs)
+        self.ymax = openmc.YPlane(y0=ymax, **kwargs)
+        self.zmin = openmc.ZPlane(z0=zmin, **kwargs)
+        self.zmax = openmc.ZPlane(z0=zmax, **kwargs)
+
+    def __neg__(self):
+        return (+self.xmin & -self.xmax &
+                +self.ymin & -self.ymax &
+                +self.zmin & -self.zmax)
+
+    def __pos__(self):
+        return (-self.xmin | +self.xmax |
+                -self.ymin | +self.ymax |
+                -self.zmin | +self.zmax)
+
+
+class XConeOneSided(CompositeMixin, openmc.Surface):
+    _surface_names = ('cone', 'plane')
+
+    def __init__(self, x0=0., y0=0., z0=0., r2=1., up=True, **kwargs):
+        self.cone = openmc.XCone(x0, y0, z0, r2, **kwargs)
+        self.plane = openmc.XPlane(x0)
+        self.up = up
+
+    def __neg__(self):
+        return -self.cone & (+self.plane if self.up else -self.plane)
+
+    def __pos__(self):
+        if self.up:
+            return (+self.cone & +self.plane) | -self.plane
+        else:
+            return (+self.cone & -self.plane) | +self.plane
+
+
+class YConeOneSided(CompositeMixin, openmc.Surface):
+    _surface_names = ('cone', 'plane')
+
+    def __init__(self, x0=0., y0=0., z0=0., r2=1., up=True, **kwargs):
+        self.cone = openmc.YCone(x0, y0, z0, r2, **kwargs)
+        self.plane = openmc.YPlane(y0)
+        self.up = up
+
+    __neg__ = XConeOneSided.__neg__
+    __pos__ = XConeOneSided.__pos__
+
+
+class ZConeOneSided(CompositeMixin, openmc.Surface):
+    _surface_names = ('cone', 'plane')
+
+    def __init__(self, x0=0., y0=0., z0=0., r2=1., up=True, **kwargs):
+        self.cone = openmc.ZCone(x0, y0, z0, r2, **kwargs)
+        self.plane = openmc.ZPlane(z0)
+        self.up = up
+
+    __neg__ = XConeOneSided.__neg__
+    __pos__ = XConeOneSided.__pos__