Direct calculation of elasticity in the Potential Induced Breathing (PIB) model is developed. This allows calculation of elastic constants and acoustic velocities of oxides and silicates without any experimental data other than the values of fundamental constants, such a Planck's constant. The PIB model allows for spherical charge relaxation in response to the long-range electrostatic potential. This feature is not present in any other lattice dynamical model, and leads to many-body forces that break the Cauchy conditions for centrosymmetric crystals (i.e. C44=C12) without the introduction of explicit angle bending forces. The elastic properties are calculated here for corundum and stishovite. High pressure elastic instabilites are found for both corundum (&agr;-Al2O3) and stishovite (SiO2). Softening of C44 for corundum is calculated to begin at approximately 120 GPa. This may require reconsideration of the ruby fluoresecence pressure scale and recent ultra-high pressure diamond cell experiments. The high pressure instability in stishovite leads to a low pressure dependence for the aggregate shear wave velocity. ¿ American Geophysical Union 1987