A computer model of a magnetosphere in which the magnetic dipole axis points into the solar wind has been developed. The axial symmetry implied by this physical situation admits a two-dimensional treatment. The model features (1) a magnetopause in pressure balance with the solar wind, (2) an analytic asymptotic tail model to account for the distant magnetotail, and (3) a full accounting of the magnetohydrodynamic pressure in the magnetosphere. The plasma pressure is a function of the Euler potential, &agr;(=rAϕ). The principal physical result is that with an increase in the plasma pressure from zero the magnetic field configuration changes slowly at first. As the pressure increases further, the field configuration changes more rapidly until X and O lines are formed.