By using Gr¿neisen theory and third-order finite strain theory, elastic-wave velocities in olivine-pyroxene assemblages are accurately determined as a function of pressure and temperature. Equilibrium distributions of H2O fluid in mantle rocks have been determined at high pressure and temperature, and are used to estimate Vp and Vs in the olivine-pyroxene-H2O system. Importantly, velocities calculated for the peridotite-H2O system successively reproduce the absolute Vp and Vs values measured in the laboratory for dehydrated serpentinite. Known equilibrium distributions of H2O-CO2 fluid in peridotite-liquid systems allow one to estimate elastic properties of fluid-bearing mantle rocks from mineral and liquid elasticity data.