The full elastic constant tensor of orthorhombic MgSiO 3 perovskite has been determined from first principles for the first time at high pressure using the plane-wave pseudopotential method. The athermal elastic moduli, determined throughout the pressure regime of the earth's mantle (0-140 GPa) from stress-strain relations, are found to be in excellent agreement with Brillouin scattering data at zero pressure. The degree of elastic anisotropy of the mineral is found to be strongly pressure dependent. The anisotropy at first decreases with pressure and then increases showing corresponding changes in the propagation directions of the slowest compressional (P) and shear (S) waves. Comparisons with seismological observations show that a Mg-rich silicate perovskite-dominated composition can plausibly account for the radial P- and S-wave velocity structure of the lower mantle.