An analysis of the effects of fiber packing on shell-side mass transfer coefficients for axial fluid flow through fiber bundles with uniform wall concentration is presented. A combined finite element (FE)-finite difference (FD) method is used to solve the governing conservation of momentum and mass equations. Results are given for values of the Graetz number that range from the entry mass transfer limit to the well-developed limit. Effective mass transfer coefficients for randomly packed fiber bundles can be much lower than for regularly packed fiber bundles for a given fiber packing fraction and Graetz number. Regions of higher fiber packing have lower flow and experience greater mass transfer than regions of lower fiber packing. The changes in the low packing regions dominate, because of the higher flow, and lead to a reduction in the overall mass transfer coefficient.