Methods are described for calculating the effects of hydrodynamic interactions on the hindered transport of solid spherical macromolecules in ordered or disordered fibrous media. These methods are applied to a medium made up of a square lattice of straight, bead-and-string-type fibers. Hydraulic permeabilities and coefficients governing hindered diffusion and convection are obtained from a detailed hydrodynamic model, and the hindered transport coefficients are shown to be in very good agreement with an effective medium approach based on Brinkman's equation. The use of Brinkman's equation for the calculation of hindered transport rates in fibrous membranes and gels is validated further by comparing with experimental data from the literature.