An analysis of the effects of nonuniform packing on external mass-transfer coefficients for axial flows through bundles pf parallel, axially oriented fibers is presented in the entry mass-transfer limit. In this limit, one can obtain an analytic solution to the mass-transfer boundary-layer equations in terms of the velocity gradient on the fiber surface for either a constant wall flux or constant wall concentration. To explicitly calculate mass-transfer coefficients, a numerical approximation for the velocity gradient is obtained from the conservation of momentum equations using the boundary-element method. Results indicate that the effective mass-transfer coefficient depends strongly on fiber packing. Regions of higher fiber packing have lower flows and lower mass-transfer coefficients than regions of lower packing. The net effect is a dramatic decrease in overall mass-transfer coefficient relative to mass-transfer coefficients in regularly packed fiber bundles.