An analysis of the effects of fiber packing on mass transfer coefficients for axial fluid flow through fiber bundles with uniform wall flux in the well-developed limit is presented. The finite element method is used to solve the governing momentum and conservation of mass equations. The effective mass transfer coefficient depends strongly on fiber packing. Randomly packed fiber bundles have much lower mass transfer coefficients than regularly packed fiber bundles. Mass transfer rates are controlled by the lowest fiber packing regions through which most of the flow occurs.