We have recently investigated the elastic properties of five compounds generally considered as potential consituents of the Earth's lower mantle. Full elastic constant tensors of MgSiO3 and CaSiO3 perovskites, MgO, CaO, and SiO2 have been determined as a function of pressure up to 140 GPa and at zero temperature using the first principles plane wave pseudopotential method within the local density approximation. We report comprehensive comparisons of the calculated high-pressure elastic wave velocities of these phases with seismically derived lower mantle properties. The effects of iron and temperature are estimated in the case of Mg-silicate perovskite based on available experimental data. Comparison of the P and S wave velocity profiles of perovskite along a series of high-temperature isotherms to the lower mantle supports the view that this region is primarily composed of Mg-rich silicate perovskite. Our study also suggests that among the candidate phases usually considered, none are invisible. Minor phases which may be present, including magnesiow¿stite, CaSiO3 perovskite, and the high-pressure polymorphs of SiO2 and CaO, have elastic wave velocities that differ significantly from those of Mg-rich silicate perovskite and may be detectable seismically. ¿ 1999 American Geophysical Union