Finite-element, mathematical models that solve laplace's and richard's equations numerically were used to locate the phreatic surface within tailings pond embankments and to define the subsurface flow of water from the pond. Both must be known to design structurally and environmentally safe tailings dams. The permeability distribution within and beneath the embankment, the fluid potential values upgradient and downgradient from the embankment, and the geometry and elevation of an approximately impermeable layer at some depth beneath the embankment were used as computer inputs in analyzing over a dozen finite-element models of tailings dams varying structurally from simple to complex. Results predicted with the finite-element model were confirmed with measurements in a laboratory model of a tailings pond and in the field. Of particular importance to the design of safe slopes, all data indicated that the phreatic surface within a tailings dam is concave upward, a configuration opposite that in most earth dams. The close correlation between predicted and experimental values confirmed the practicability of using the finite-element technique to design safe tailings dams.