ABSTRACT A groundwater model is developed by using an explicit formulation of the two-dimensional diffusion equation of flow in porous media for a homogeneous isotropic aquifer. Appropriate sources/sinks and head/flux or permeable/impermeable boundaries can be specified. The model is stable for cell Reynolds number D less than or equal to 1. Numerical tests under a wide range of conditions show that the model is convergent only for D = 1. Hypothetical tests show that the model is able to simulate groundwater flow with excellent stability, convergence, and mass-conservation properties.