We investigate by first principles the elastic behavior of Al2O3-alumina under pressure (up to 300 GPa) in the corundum and Rh2O3 (II) phase. The results are in excellent agreement with available low pressure (<1 GPa) experimental data. The anisotropy in elasticity for corundum decreases up to 50 GPa and then increases slowly with pressure whereas for the Rh2O3 (II) phase the anisotropy increases monotonically with compression. Strong shear wave anisotropy in the Rh2O3 (II) phase is found to be associated with the relatively small c55 modulus, and its softening at high pressures. Unlike corundum, the directions of the fastest and slowest wave propagation, and the maximum polarization anisotropy of Rh2O3 (II) phase remain unchanged with pressure. At the corundum to Rh2O3 (II) phase transition pressure (78 GPa at O K), the anisotropy increases by more than 100% but the density and wave velocities increase only by 2%. The calculated (O K) densities and wave velocities at lower mantle pressures are slightly larger (by 5%) than the corresponding seismic profiles. Our results suggest that the presence of free Al2O3 in small amount in the lower mantle may not be detected in seismic density and velocity profile. However, its anisotropy may produce a detectable signal, particularly, at pressure conditions typical of the D″ region.