We study subsurface storm flow from a planar hill slope, a problem that is similar hydraulically to lateral flow toward drains in landfills. Our analysis is based on the linearized one-dimensional Boussinesq equation (Dupuit-Forchheimer approximation), which is extended to allow for leakage through the underlying barrier. This linear advection-diffusion equation has a greater range of validity than the kinematic wave equation. Stating it in terms of the discharge, the variable of primary hydrologic interest, we integrate it numerically, using an adaptation of the Muskingum-Cunge routing scheme. A single-step computation of the outflow hydrograph, which combines the convenience of an analytical solution formula with acceptable accuracy, is proposed as a design tool and as a means of parameterization of drainage from hill slopes. Depth profiles are determined afterwards by a simple integration of Darcy's law. Examples of the buildup and recession phases, with and without leakage, demonstrate the application of the computational method. ¿ 1998 American Geophysical Union