Compressional and shear wave velocities have been measured in Westerly granite under conditions of high temperature to 500¿C, high confining pressure to 5 kbar, and independently controlled pore water pressure. Measurements in a dry sample show that at a given temperature, confining pressure has a larger accelerating effect on compressional wave velocity (Vp), while at a given confining pressure temperature has a larger retarding effect on shear wave velocity (Vs). The combined effects of temperature and pressure act to increase Poisson's ratio in a dry rock. Increasing the temperature of a sample that contains pure water at low pressure causes a continuous decrease in the bulk modulus (&kgr;) and Vp, while the shear modulus (μ) and Vs are affected only by the temperature of the crystalline matrix. The low Vp and nearly unchanged Vs cause a decrease in Poisson's ratio. Under otherwise identical conditions of pressure and temperature high pore fluid pressure causes a decrease in μ and Vs, while vp is less affected and Poisson's ratio increase. This trend continues until at high temperatures the bulk modulus of the pore water decrease and results in a decrease in Vp. Gassmann's theory is found to predict closely the compressional and shear wave velocities of saturated porous samples from the elasticity of their dry crystalline matrix and the known properties of water. Finally, time-dependent compressional velocities may be caused in laboratory samples by solution of quartz in supercritical pore water.