We present a predictive model of the magnetopause, constructed using three-dimensional global MHD simulations of the magnetosphere over a range in solar wind dynamic pressure and the north-south component of the interplanetary magnetic field (IMF BZ). The magnetopause is identified in the simulations using electric current intensity, thermal pressure, and magnetic field line mapping. The magnetopause is fitted by least squares to an ellipse in each plane, and a fully three-dimensional magnetopause surface is constructed by assuming an elliptical cross section at intermediate clock angles. There is considerable flaring of the magnetopause dependent on BZ in the noon-midnight meridian plane due to reconnection but virtually no flaring in the equatorial plane. Despite this asymmetry, when averaged over clock angle, the model shows a general agreement with recent (axisymmetric) empirical magnetopause models and predicts observed magnetopause crossings with about the same accuracy as the empirical models. Unlike these empirical models, our model can directly investigate asymmetries between the meridian and equatorial planes. The subsolar distance, directly measured from the simulations, varies linearly with BZ for both northward and southward interplanetary magnetic field, as do distance to the magnetopause on the flanks. Magnetospheric plasma pressure causes these distances to scale with dynamic pressure by a power law whose exponent is a bit less than -1/6 on the dayside, but little deviation from this ideal Chapman-Ferraro value is seen in the magnetotail. These uniform changes with BZ lead to approximate conservation of (1) magnetopause shape in the dayside equatorial plane, (2) projected area in the dayside meridian plane, and (3) magnetopause cross-sectional area in the dawn-dusk plane. The dawn-dusk magnetopause cross section is nearly circular on average, but cross sections in the tail are elongated in the Z direction on average.¿ 1997 American Geophysical Union