A theoretical analysis of the effect of random fiber packing on shell flow distribution, associated shell-side concentration boundary layers, and ultimate performance of shell-fed hollow-fiber gas separation modules is presented. Specifically the relationship between recovery and product oxygen mole fraction is evaluated for nitrogen production from air. Results show that for commercial hollow-fiber membrane modules, random fiber packing is not detrimental to performance relative to the performance of an ideal module. However, poorer performance is predicted for modules with higher permeances. Permeances will have to increase by over an order of magnitude, though, before the effect becomes significant.