Subsurface flow from a hillslope can be described by hydraulic groundwater theory, as formulated by the Boussinesq equation. Solution of its linear version brings out some of the essential features of this phenomenon. Arbitrary inputs can be accommodated by simple convolution of the sudden drawdown problem. The relative magnitude of the driving mechanisms, namely the streamwise pressure gradient, resulting in diffusion and gravity (i.e., slope), resulting in advection, can be determined by a simple dimensionless parameter. ¿ American Geophysical Union 1994