In this paper the two-dimensional flow of fresh and salt water through a homogeneous aquifer is considered. The two fluids are assumed to be separated by a sharp interface. They differ only in their specific weight. This difference induces a flow in the aquifer which in turn causes a motion of the interface. We present a mathematical formulation of this problem which consists of a Poisson equation for the stream function coupled to a time evolution equation for the moving interface. The equation for the stream function is solved by means of a finite-element method while a predictor-corrector method (the Saß scheme) is used for the discretization of the equation for the interface.