Surface roughness on membranes has been shown to increase flux, in part because surface area was increased. However, experimental studies of the relationship between flux and surface roughness have produced contradictory results in which flux did not always increase with increased surface roughness. Increases in flux that are greater than the increase in surface area also have been reported, with hydrogen flux through palladium and palladium-copper films as an example. A mathematical model was developed to examine two-dimensional diffusion through a roughened membrane when the surface is at local equilibrium with the feed. By comparing the results to a one-dimensional diffusion model, contributions of diffusion parallel to the plane of the membrane could be separated from that of a shorter diffusion path through the thin regions. Although lateral diffusion can be significant, more often the presence of thinner regions was the dominant factor for increased flux. The model calculations predict that membrane flux can increase by more or less than the increase in surface area depending on the geometry of the surface roughness. For the geometry of the surface structures in the hydrogen permeation experiments, model calculations indicate that flux increases larger than the increase in surface area could occur. (C) 2012 Elsevier B.V. All rights reserved.