The ability of local density functional theory to predict properties of oxide minerals at high pressures is tested by computing some thermodynamic properties of MgO and CaO in the B1(NaCl) and B2(CsCl) structures. Both static and dynamic contributions to the equations of state of computed ab initio, thus yielding predictions that are completely independent of data. Except for a possible overestimate of the density of B2 phases, the theoretical room temperature isotherms, shock-wave Hugoniots and zero pressure density and elastic parameters are in excellent agreement with data. The predicted B1-B2 transformation pressure for CaO is 32 GPa, compared to the experimental value of 61 GPa. The corresponding pressure of MgO is 205 GPa and is believed to be a lower bound on the actual transformation pressure.