A computational procedure is introduced for calculating the magnetic fields produced by virtually any distributed system of electrical currents. This procedure is being applied to the modeling of magnetic fields produced near the earth and on its surface by horizontal currents flowing in the ionosphere and by the so-called Birkeland currents flowing along the geomagnetic field at high magnetic latitudes. This report describes briefly the principles that underlie the technique and illustrate the results obtained when the model is applied to the interpretation of perturbation fields being mesured by the polar-orbiting magnetic fields satellite (MAGSAT). Even for a very simple assumed current distribution we calculate magnetic field residuals whose large-scale features are similar to those deduced from MAGSAT measurements. A predominately sunward magnetic perturbation is obtained over the region poleward of the Region 1 current system as a natural consequence of balanced Region 1 and Region 2 currents. The model predicts the existence of low-latitude magnetic effects of auroral currents that represent potential sources of error for spherical harmonic representations of the geomagnetic field.