Physically-based models of catchment hydrology are computationally demanding. the cost of even small scale simulations of multidimensional subsurface flow problems is often considered too high and yet May, be important if one is to appreciate the complex flow pathways in heterogeneous catchments. This is likely to be the case for problems concerned with transport of chemical substances in soils, in particular those with some localized origin. Recent advances in computer hardware technology and numerical algorithms are beginning to make detailed simulations more feasible. We discuss here issues relating to using these new tools in modelling hillslope flow processes and document an example three-dimensional simulation of a heterogeneous Darcian headwater.