In this study, based on the results obtained from laboratory measurements of compressional and shear wave velocities on 5 sandstone samples from Gadvan formation and 5 limestone samples from Sarvak formation under different confining pressures in both dry and water-saturated states, the effect of both pressure and saturation on velocities have been investigated. The measurements have been performed in Technology Research Center (TRC) of Japan National Oil Corporation. Gassmann's theory is applied to the data to predict the saturated velocities from dry ones and a good agreement was found. The data also demonstrates simple relationships between compressional and shear wave velocities for both sandstone and limestone samples separately. A linear relationship for sandstones and a nonlinear one for limestones.