In this paper we continue previous studies of the closure problem for two-phase flow in homogeneous porous media, and we show how the closure problem ca n be transformed to a pair of Stokes-like boundary-value problems in terms of 'pressures' that have units of length and 'velocities' that have units of length squared. These are essentially geometrical boundary value problems that are used to calculate the four permeability tensors that appear in the volume averaged Stokes' equations. To determine the geometry associated with the closure problem, one needs to solve the physical problem; however, the closure problem can be solved using the same algorithm used to solve the physical problem, thus the entire procedure can be accomplished with a single numerical code.