A digital simulation model has been presented for locating the steady state stable brine cone position beneath partially penetrating wells tapping from the fresh water zone overlying a saline zone in an unconfined anisotropic aquifer. A graphical procedure developed by Morris Muskat has been converted into a numerical one and is used to successively approximate the brine cone position. The truncation in the fresh water zone both due to the brine cone and the depression in the water table are taken care of by repeated adjustment of the hydraulic conductances of the affected branches in the numerical model of the aquifer. An iterative version of the alternating direction implicit method has been used to solve the flow equations repeatedly till successively modified fresh water flow zones converge within a specified tolerance level. The results from the simulation model for a range of expected field conditions of aquifer, well and fluid density contrast have been presented in the form of graphs making use of appropriate non-dimensional parameters. These results can find applications in designing wells so that the discharge from those wells are limited to levels below which fresh water alone is drawn without any contamination by the underlying salt water.