Numerical descriptions of shock wave induced flows obtained with a two-dimensional Lagrangian finite difference code are compared in detail with experimental data obtained via the lateral relaxation method for polycrystalline magnesium oxide (MgO) to a pressure of 360 kbar. The equation of state used for MgO was assumed to be of the Mie-Gr¿neisen form, and detailed comparison of experimental and calculated data was used to obtain refined values of the shear strength and shear modulus of MgO at high pressures. The best fitting rheological model for MgO was characterized by a shear strength which decreased from a value of 26 kbar at 16.5-kbar mean stress to 13.5 kbar at 360-kbar mean stress along the principal Hugonioi curve. The first and second pressure derivatives of the shear modulus, when the shear modulus is evaluated as a quadratic function of pressure, yield (∂μ/∂P) =2.44 and μ (∂2μ/∂P2) =1.7¿3.0. The uncertainties in the determination of μ (∂2μ/∂P2) have been reduced by a factor of 5 over previous estimates.