Ultrasonic velocities of single crystal MgO (periclase) and MgAl₂O₄ (spinel) were measured up to 7.78 GPa and 6.16 GPa, respectively, under hydrostatic pressure. The present success was attained by making various technical developments, such as a liquid-solid hybrid system and indium bond between sample and buffer-rod. Analytical procedures were also developed both in required corrections for apparent travel times, and in formulation of pressure effect on elasticity. A distinct shear softening was found in MgAl₂O₄, and was predicted to occur in MgO beyond 30 GPa. Isothermal equation of state of MgO was derived by combining the present results with shock hugoniot. Heat capacity, Grüneisen constant, and coefficient of thermal expansivity of MgO at high pressures were calculated by means of a new model equation of state. Negative thermal expansivity is expected to take place in MgO above -50 GPa. The pressure derivative of rigidity of γ-Mg₂SiO₄ is estimated to be 0.56-1.0 by means of a lattice dynamic analogy with MgAl₂O₄; the lower margin of the estimate leads to the pressure-induced shear softening of γ-Mg₂SiO₄ in the earth's upper mantle.