This article presents a theoretical study of the dependence of the magnetopause shape and field on the dynamic pressure of the solar wind. The magnetopause surface (assumed to be axisymmetric) is determined by requiring the plasma pressure outside, estimated by the ''Newtonian approximation,'' to be balanced by the magnetic pressure inside. The magnetic field inside is given by the sum of (1) the Earth's internal field, (2) the field from various magnetospheric current systems (cross-tail current, ring current, etc.) as given by an empirical model, and (3) the field due to magnetopause currents. The magnetopause field is a function of the magnetopause shape and is updated each time this shape is adjusted toward pressure balance. In previous studies of this kind, only dipole and magnetopause fields were incorporated. This is the first three-dimensional solution of the problem to include the cross-tail current and thus to obtain a realistic magnetotail configuration. The results of this study are twofold. First, the shape of the magnetopause surface is computed under a variety of conditions. The resulting shapes are compared with fits to observed magnetopause crossings, and the scaling of magnetopause position on solar wind dynamic pressure is determined. Second, the model that results can be viewed as an improved version of the empirical model that was used as input, in that the magnetic field in the vicinity of the magnetopause (where empirical models have less guidance from data) is made more realistic. ¿ American Geophysical Union 1996