The variation in dilatational and rotational velocities in rock samples with pressure and temperature has been studied. The measurements were taken at pressures from 1 bar (atmospheric) to 5,000 bars, and temperatures of 25 degrees C. to 200 degrees C. for all samples and up to 300 degrees C. for two samples. We can thus reach a pressure equivalent to some 18 km or 60,000 feet of burial but our highest available temperature probably at most corresponds to no more than 8-9 km.The measured rotational velocities check very well with independent measurements. Laboratory measurements of the dilatational velocity are not available for comparison. From the measured dilatational and rotational velocities, the elastic moduli and Poisson's ratio may be computed. Values of Poisson's ratio are tabulated for all samples. In general, highly quartzitic rocks have low values 0.13-0.20 whereas the majority of rocks have values in the range 0.26-0.33.The effect of interstitial water has been investigated in one sandstone and one limestone. The sandstone shows an increase in velocity at low pressure and a decrease at high pressure whereas the limestone shows the opposite effect.