We have simulated the steady state magnetospheric configuration which results when solar wind plasma impinges on a magnetic dipole. In our calculation, the MHD equations were solved self-consistently by a large scale code which employs Rusanov's method to produce a three-dimensional model of the magnetospheric fields and plasma. This simulation, in which the interplanetary magnetic field was assumed to be zero, reproduced many of the observed magnetospheric features including the bow shock, magnetopause and plasma sheet. In particular, the calculated magnetic field is consistent with quiet time observations. The currents in the stimulated magnetosphere are remarkably similar to those from semi-empirical magnetic field models.