[518.1.1] Numerical solutions were calculated for the coupled system (15) of nonlinear partial differential equations obtained by macroscopic constitutive modeling of two phase flow. [518.1.2] The equations are based on the concept of hydraulic percolation of fluid phases. [518.1.3] The results illustrate the ability of the new theory to describe drainage and imbibition occurring simultaneously within the same sample, or sequentially at the same position inside a porous medium. [518.1.4] Stationary solutions are compared to predictions from the traditional theory and significant differences are found. [518.1.5] We emphasize that the numerical solutions are approximate. [518.1.6] We encourage experimental groups to measure residual fluid distributions during or after immiscible displacement. [518.1.7] Such measurements would allow us to test our theoretical predictions against experiment.