A management concern with waste dumps is the movement of leachate into local groundwater systems. This paper presents a model to predict the saturated-unsaturated flow of water within such waste dumps. The model predicts moisture movement when the surface of the dump is bare and when it has revegetated. For the bare state, the evaporation rate is related to a number of complex processes, including atmospheric transport, radiation balance, and subsurface water supply in either liquid or vapor forms. Transpiration from the revegetated heap is related to the leaf area index and rooting depth, both of which change as plants grow. Mechanisms influencing vapor transport are considered in some detail, and a nonequilibrium approach employed to explain combined liquid and vapor movement. The mathematical problem consists of solving a system of coupled, nonlinear, partial differential equations which are related dynamically to the surface boundary conditions. The boundary conditions are determined by a combination of meteorological variables as well as the type and amount of plant cover. A moving node finite element method is presented which has the capability of automatically relocating nodes to areas of numerical difficulty. This method is validated through comparison with a proven solution to the unsaturated flow equation. The next paper in this series presents the application of the model to oil shale waste dumps. ¿ American Geophysical Union 1993