A theoretical analysis of shell-side flow effects on the performance of hollow-fiber gas separation modules is presented. The theory uses Darcy's law to relate fiber packing, pressure fields, and velocity fields within the shell. The resulting shell conservation equations are coupled to the lumen conservation equations through the permeation relationship. This two-dimensional (2-D) analysis quantifies the performance penalty associated with gas distribution across the fiber bundle at the shell inlet and outlet. Theoretical predictions for the production of nitrogen from air in a commercial shell-fed module are closer to experimental data than predictions obtained assuming one-dimensional (1-D) plug flow. Fluid flows primarily across fibers near the inlet and outlet ports, and along fibers between ports. Nitrogen composition increases along fluid streamlines, which leads to axial and radial concentration variations within the fiber bundle. Diffusional contributions to shell mass transfer are small for the modules considered here.