Using the RUS technique called rectangular parallelepiped resonance, a large database on elastic constants and associated thermoelastic parameters extending from 300 K up to as high as 1800 K (P=0) has been established at UCLA. Temperature derivatives of the C[inf ij]'s have been determined with considerable precision. It has been shown how the pressure derivatives of elastic constants ((cursive beta)C[inf ij]/(cursive beta)P)[inf T] can be approximated from ((cursive beta)C[inf ij]/(cursive beta)T)[inf P]. Agreement with experiment is quite good in some cases. Extending this method to high pressure (>3 GPa) requires evaluation of the volume dependence of the parameter, ((cursive beta)P/(cursive beta)T)[inf V]=(alpha)K[inf T], where (alpha) is thermal expansivity and K[inf T] is the isothermal bulk modulus. Again, this is done from temperature C[inf ij] data, but it requires one datum on pressure, K[inf 0][sup ']=((cursive beta)K[inf T]/(cursive beta)P)[inf T] (P=0). From the data, the temperature at which (alpha)K[inf T] becomes independent of volume was predicted. The theory agrees well with experiment for all solids tested (NaCl, MgO, Al[inf 2]O[inf 3], Mg[inf 2]SiO[inf 4], CaO).