Full elastic constant tensors of three high-pressure polymorphs of silica: stishovite, CaCl2-type and columbite-type (&agr;-PbO2 structure); are determined at lower mantle pressures from first-principles using the plane wave pseudopotential method within the local density approximation. The calculated zero pressure athermal elastic moduli are within a few percent of the experiments. We find that the elastic properties of silica are strongly pressure dependent. The shear wave velocity decreases rapidly (by 60%) and the anisotropy increases rapidly (by a factor of five) between 40 and 47 GPa prior to the transition from stishovite to the CaCl2 structure at 47 GPa. At this phase transition, the isotropically averaged shear wave velocity changes discontinuously by 60%, while the S-wave polarization anisotropy decreases by a factor of two. The transformation of the CaCl2 phase to the columbite phase at 98 GPa is accompanied by a discontinuous change of 1--2% in elastic wave velocity and decrease by a factor of two in anisotropy. We suggest that even a small amount of silica in the lower mantle may contribute significantly to observed seismic anisotropy, and may provide an explanation of observed seismic reflectivity near 1000 km. ¿ 1997 American Geophysical Union