The lattice Boltzmann method (LBM) is used to simulate viscous fluid flow through a column of glass beads. The results suggest that the normalized velocity distribution is sensitive to the spatial resolution but not the details of the packing. With increasing spatial resolution, simulation results converge to a velocity distribution with a sharp peak near zero. A simple argument is presented to explain this result. Changes in the shape of the distribution as a function of flow rate are determined for low Reynolds numbers, and the large-velocity tail of the distribution is shown to depend on the packing geometry. The effect of a finite Reynolds number on the apparent permeability is demonstrated and discussed in relation to previous results in the literature. Comparison with velocity distributions from NMR (nuclear magnetic resonance) spectroscopy finds qualitative agreement after adjusting for diffusion effects in the NMR distributions. ©1998 American Institute of Physics.