A system has been developed for determining precisely the dilatational and shear‐wave group velocities in rock samples subjected to hydrostatic confining and internal pore pressures independently to 10,000 psi. Pulses of polarized shear waves of 500‐kc/sec carrier frequency are produced and detected by axially polarized ceramic transducers attached to Pyrex glass prisms mounted in pressure‐sealed cells at each end of the rock sample. Complete mode conversion from dilatational waves to polarized shear waves, and vice versa, occurs at the free surfaces of the prisms. Pulses of dilatational waves of the same carrier frequency are produced and detected by axially polarized ceramic transducers mounted in a separate pair of pressure‐sealed cells which are attached at each end of the sample. Dilatational and shear‐wave velocities have been measured on three dry sandstones in directions perpendicular and parallel to the bedding plane. Two of the rocks were found to exhibit anisotropy in the form of transverse isotropy with the bedding plane as the plane of symmetry, and the third to exhibit isotropy. A reduction was noted in the degree of anisotropy for the two rocks as the hydrostatic confining pressure was increased. The influence of pore liquid saturants on the velocities of waves in several sandstones has been investigated. It has been concluded that the velocities in these rocks depend significantly on interfacial surface phenomena, relaxation behavior of the liquid saturants in small cracks, and upon interaction between the saturant and interstitial detrital material. At high hydrostatic pressures on the rock frame, the effects of interfacial surface phenomena and relaxation behavior of the liquid saturants tend to decrease. The influence of changes in pore fluid pressure on the velocities of waves has been studied. Provided the effects of mechanical hysteresis of the rock were avoided, the velocities in sandstones were found to depend on the simple difference between the hydrostatic confining and internal pore pressures.