A linear complementarity theory is proposed for the coupled treatment of groundwater seepage and surface runoff along a sloping plane ground perturbed by irregular channels. Steady downslope routing is applied to the two-dimensional overland flow, while Green functions are used to relate the three-dimensional groundwater motion to the surface drainage and recharge distribution. The coupling between the surface and subsurface components is formulated as a linear complementarity problem. The algorithms needed to compute useful solutions are presented and validated. Two variants of the theory are addressed, one applicable to large-scale problems in which capillary effects can be neglected and the other to small-scale processes for which the range of variation of the topography does not exceed the capillary fringe. Linearized theories for these two cases are found to be very close in their structure and in their predictions, providing a rigorous basis for the representation of field-scale processes by laboratory-scale analogues. Predictions from the theory are compared with detailed experiments in which groundwater sapping was monitored using a video camera and a laser sheet scanning apparatus.