A general model describing three-dimensional lateral preferential water flow in a hillslope with soil pipes was developed. Matrix flow and pipe flow were regarded as separate flow systems and computed using the governing equations (Richards' and Manning's equations, respectively), while simultaneously considering the interaction between these two flow systems. The model accommodates both partially filled and full pipe flow, seepage into the pipe, and backflow from the pipe into the surrounding soil matrix. Simulations were conducted for conditions outlined in an earlier bench-scale experiment, including differing internal roughness configurations within the pipe. Both groundwater levels and preferential flow under steady state conditions were simulated for different roughness elements within the soil pipe; previous models have not simulated such conditions. Six different pipe arrangements were also simulated: no pipe (uniform matrix flow), single straight pipe, two sets of discontinuous pipes, branched pipes, and unopened pipe. Branched pipes had the highest discharge, and even the unopened pipe contributed to an enhanced total discharge compared to the no pipe simulation. These simulations demonstrated the versatility of the model under the steady state conditions, although the model can also be applied to transient conditions.