Mathematical models that solve the Laplace or Richards' equation numerically have been used in two ways: to locate the phreatic surface within a mine tailings pond embankment, and to define the subsurface flow system that transports water outward from the pond. Input data needed for the finite element model include the saturated hydraulic conductivity (permeability) distribution within, and beneath, the embankment; the fluid potential values at both upgradient and downgradient boundaries of the embankment; and the geometry and elevation of an approximately impermeable layer at some depth beneath the surface of the embankment. This technique has been applied to a tailing disposal system in northern Washington. Laboratory tests were used to obtain permeability values from samples collected by the Shelby tube method. Pond boundaries were examined by drillholes and piezometers. Piezometers were also used to validate the configuration of the phreatic surface predicted by the model. Of particular importance to slope stability analysis is the fact that both the model and the check piezometers indicate that a significant portion of the phreatic surface within the embankment is concave upward. Experimentation with the finite element model revealed that the concave upward portion is a consequence of the upstream boundary in a tailings pond being a flow line and embankment permeability being lower near the upsteam boundary; the upstream boundary of the flow region in an earth dam is normally an equi-potential line.