Ultrasonic P-wave attenuation and phase velocity dispersion have been estimated for 29 samples of sandstones and 13 samples of shales from a Glenn Pool oil reservoir using a pulse transmission technique. The measurements were performed under effective pressures from atmospheric to 15 MPa. There is a strong correlation between attenuation co-efficient and phase velocity dispersion. Even though the observed attenuation may deviate from a "constant Q" model, it generally agrees with a minimum-phase prediction. Attenuation in the water-saturated sandstones increases with porosity and permeability. We found no correlation between the attenuation and clay content within the sandstone subset. Attenuation in the shales is much less than that in the sandstones. This difference may be used in reservoir characterization.