The flux per volume across selective membranes can potentially be increased by at least five times using corrugated membranes. This increase is important because membrane selectivity is often inversely related to membrane Aux. The flux across a selective membrane which is hampered by low permeability can be increased by making the membrane thin and by having a large membrane area per volume, e.g., by using hollow fibers. Where these flux increases are insufficient, membrane corrugations could supply further gains. This paper derives a theory predicting these increases. The theory is verified for pervaporation of aqueous chloroform, ethanol and other solutes across macrocorrugated polydimethylsiloxane membranes. The results supply criteria which must be met by any nanocorrugated membranes.