This thesis concerns the use of mathematical models of the rainfall-riverflow process to simulate peak flows on hydrologically small catchments. It seeks to determine whether a more detailed description of the subsurface zone of a catchment will improve the performance of such a model. A numerical solution to Richards' equation for flow in an unsaturated porous medium applied to a one-dimensional, vertical column of soil was used to replace the subsurface components, including infiltration, of the Stanford Watershed Model. The performance of this Amended Model was compared with that of the Stanford Model itself, using rainfall and river flow data from three New Zealand catchments. Published solutions to Richards' equation in two dimensions were also examined to estimate the usefulness of extending this approach. The amendments reduced the number of fitted parameters from five to four, while the performance of the Amended Model proved to be comparable to that of the Stanford Model in spite of restrictions imposed by the one-dimensional formulation. The two-dimensional solutions to Richards' equation were found to offer more versatility of behaviour and physical relevance than the one-dimensional solution. It was therefore concluded that a model based on the two-dimensional solution would be superior to the Stanford Model, and that more attention should be paid to the subsurface processes by model-builders.