Global, three-dimensional, ideal MHD simulations of Earth's bow shock are reported for low Alfven Mach numbers MA and quasi-perpendicular magnetic field orientations. The simulations use a hard, infinitely conducting magnetopause obstacle, with axisymmetric three-dimensional location given by a scaled standard model, to directly address previous gasdynamic (GD) and field-aligned MHD (FA-MHD) work. Tests of the simulated shocks' density jumps X for 1.4≲MA≲10 and the high MA shock location, and reproduction of the GD relation between magnetosheath thickness and X for quasi-gasdynamic MHD runs with MA≫MS, confirm that the MHD code is working correctly. The MHD simulations show the standoff distance as increasing monotonically with decreasing MA. Significantly larger as are found at low MA than predicted by GD and phenomenological MHD models and FA-MHD simulations, as required qualitatively by observations. The GD and FA-MHD predictions err qualitatively, predicting either constant or decreasing as with decreasing MA. This qualitative difference between quasiperpendicular MHD and FA-MHD simulations is direct evidence for as depending on the magnetic field orientation &thgr;. The enhancement factor over the phenomenological MHD predictions at MA~2.4 agrees quantitatively with one observational estimate. A linear relationship is found between the magnetosheath thickness and X, modified both quantitatively and intrinsically by MHD effects from the GD result. The MHD and GD results agree in the high MA limit. An MHD theory is developed for as, restricted to sufficiently perpendicular &thgr; and high sonic Mach numbers MS. It explains the simulation results with excellent accuracy. Observational and further simulation testing of this MHD theory, and of its predicted MA, &thgr;, and MS effects, is desirable. ¿ American Geophysical Union 1995