We investigate the structural and elastic properties of CaO up to 140 GPa using the plane wave pseudopotential method within the local density approximation. Free energy comparison suggests that the transition from the low-pressure sodium chloride (B1) to the high-pressure cesium chloride (B2) structure in CaO occurs at 58 GPa, which falls within the experimental range of 53--70 GPa. The zero-pressure values and initial pressure dependences of the calculated athermal elastic moduli compare favorably with the experiments. We find that the elastic properties of the two phases vary differently with pressure. The degree of the anisotropy strongly increases with pressure in the B1 phase (due to softening of c44), whereas it strongly decreases in the B2 phase. However, the sign of anisotropy and the propagation directions of the extremum wave velocities remain unchanged with pressure. Both compressional and shear wave velocities of CaO are substantially lower than the seismic velocities throughout the Earth's lower mantle, suggesting that CaO is unlikely to be present in the mantle in large amounts. ¿ 1998 American Geophysical Union