The hydrodynamic transport properties of hard‐sphere dispersions are calculated for volume fractions (&fgr;) spanning the dilute limit up to the fluid–solid transition at &fgr;=0.49. Particle distributions are generated by a Monte Carlo technique and the hydrodynamic interactions are calculated by Stokesian dynamics simulation. The effects of changing the number of particles in the simulation cell are investigated, and the scaling laws for the finite‐size effects are determined. The effects of using various levels of approximation in computing both the far‐ and near‐field hydrodynamic interactions are also examined. The transport properties associated with porous media—permeabilities and hindered diffusion coefficients—are determined here. The corresponding properties of freely mobile suspensions are determined in a companion paper [Phys. Fluids31, xxxx (1988)].