Theory is developed for hillslope drainage and is applied to the condition of sudden drawdown at the aquifer outlet. The equations for prediction of cumulative outflow volume, flow rate, and water table profile are based on the Boussinesq approximation for subsurface water flow above a sloping impermeable layer. The advantages of the theory presented here are that the assumption of a long, thin aquifer is unnecessary; the same equations apply to both sloping and horizontal aquifers; and the equations contain only parameters that are easily measured or estimated: slope, drainable porosity, saturated hydraulic conductivity, and layer thickness. The accuracy of the outflow equations is illustrated by a series of laboratory experiments. ¿ American Geophysical Union 1993