The differential equation describing the flow of the solution phase in a partially saturated porous medium can be solved numerically to predict the time and spatial distributions of water content and pressure head which would result from imposed initial and boundary conditions. Most porous media have a highly hysteretic water content-pressure head relationship, and since natural boundary conditions induce hysteretic flow systems, hysteresis should be accounted for in solutions of the flow equation. Good agreement found between the predicted and measured values for the slow drainage-rewet experiment indicated that under the conditions of this experiment the unsaturated flow equation is an adequate description of the flow process. The numerical solution used was an adequate solution of the flow equation for a nonuniform medium. The scale of the nonuniformity in the medium used was rather small.