A finite element model simulating runoff and soil erosion from agricultural lands is developed. The computational efficiency and stability of various numerical schemes used for time integration are critically examined employing L2 and Chebycheff (Chebyshev) norms. Predictor-corrector and fully implicit schemes are found to give the least values of norms, thereby permitting larger time steps. A finite element solution of the one-dimensional Richards equation with a sink term simulates rain infiltration and soil moisture balance in cropped fields. A criterion to ensure stability and convergence of the solution is suggested. A finite element solution of the sediment continuity equation in conjunction with a fully implicit scheme for time integration and Yalin's equation for sediment transport capacity is developed to simulate soil erosion. The potential of the model to reasonably simulate runoff and soil erosion is demonstrated by comparing the finite element solutions with the analytical solutions under simplified configurations and with experimental data. ¿ American Geophysical Union 1994