We present a global model of the magnetic field of the magnetosphere that includes the effects of the Chapman-Ferraro currents at the magnetopause. In contrast to earlier models, the magnetopause shape is arbitrary, thus allowing the use of more realistic geometries. The internal magnetospheric field model of Hilmer and Voigt [1993>, is completely shielded within the magnetopause by solving the Laplace equation with Neumann boundary conditions using a finite difference method on a non-orthogonal, curvilinear grid. The resulting model magnetosphere is perfectly closed although the method can also be applied with more general boundary conditions, to generate a set of open models based on the approach of Toffoletto and Hill [1989, 1993>. The purpose of this paper is to demonstrate the feasibility of a purely numerical approach to solving the Chapman-Ferraro problem with arbitrary magnetopause shape and boundary conditions. ¿ American Geophysical Union 1994