The molecular flow symmetry through an arbitrarily shaped pipe is mathematically considered. An extension of Clausing's method creates a new framework that unifies both the diffuse and beam reflections. Using this framework, the author shows that only the cosine law of reflection preserves the symmetry for diffuse reflections; for beam reflections, there are innumerable reflection rules preserving the symmetry, provided that the molecularflux is conserved in a collision with the pipe wall. If the molecular flux is not conserved, i.e., the pipe wall is adsorbent, only five reflection rules remain for preserving the symmetry. (c) 2007 American Vacuum Society.