We have developed a technique for including large-scale magnetospheric current systems in magnetic field models. In this paper, we incorporate the Region I and Region II Birkeland current systems into the Source Surface Model (SSM) of the terrestrial magnetosphere. The original SSM was a prescribed-magnetopause model that used a spherical harmonic expansion and a variational principle to obtain the magnetic field in the near-Earth region. Field lines in the tail were constructed geometrically. This model is ideal for studying the effects of Birkeland currents since it has a well-defined boundary between open and closed field lines, magnetopause shielding currents separate the geomagnetic and interplanetary magnetic fields in the absence of a specified connection between the two, and Birkeland currents are not included in the model either implicitly or explicitly. The Region I and II Birkeland currents are added to the model using a series of field-aligned, infinitely thin wire segments. The magnetic field produced by these currents is calculated from the Biot-Savart law and its normal component on the surface of the magnetopause is shielded (minimized) by image currents carried on wires placed outside the magnetosphere. The result of these added currents is a sunward shift of the separatrix between open and closed field lines. Since Region I currents are regarded here as flowing on the separatrix, this shift necessitates an iteration of our procedure. Three iterations were required to reach a satisfactory solution in our case. We find that inclusion of Birkeland currents in the SSM results in a northward Bz in the near-midnight tail region, and a southward Bz at the flanks. The closure of previously open flux near midnight accounts for the sunward shift of the separatrix. Moreover, the sunward shift is found to increase with increasing Birkeland current strength by an amount that agrees with observations of the auroral oval. ¿ 1998 American Geophysical Union