The flow of recharge-induced shallow groundwater over an impermeable boundary is a basic process in hillslope hydrology, which has usually been simplified by taking the boundary as having a constant slope. Previously published equations in curvilinear coordinates have been reduced here to a single equation for shallow groundwater flow over an impermeable boundary with continuous curvature, subject to conditions. The equation has been verified by comparison with a finite difference solution of the steady flow case, and with a range of experimental data from a viscous flow physical model, for both steady and transient flows. The results show that, while the bed profile affects flow depths, it has relatively little impact on the outflow hydrograph. It was found that the outflow is closely approximated by a power relationship with the volume in storage, and this leads to a simple algorithm for predicting the outflow hydrograph under conditions of variable recharge.