Salt-water upconing describes the phenomenon where salt water is transported vertically upward under a well in response to pumpage in a fresh-water aquifer underlain by salt water. Sharp interface methods have been used successfully to describe the physics of upconing. A finite-element model is developed to simulate a sharp interface for determination of the steady-state position of the interface and maximum permissible well discharges. The model developed is compared to previous published electric-analog model results of Bennett and others (1968). Both methods are applied to a test case at Truro, Massachusetts, where maximum permissible discharges are determined by the finite-element model to range from 0.47 to 1.05 cubic feet per second for the Test Site No. 4 location.