Simple explicit solutions of the dynamical equations for a prestressed solid under horizontal compression in a gravity field are derived to establish the magnitudes of two factors influencing seismic wave propagation velocities: (1) The overburden pressure which, at depth z, leads to wave velocity changes of order &rgr;gz/μ, where p is rock density and μ is the rigidity. Compressional velocity increases with depth, whereas shear velocity decreases: at depths of the order of 150 km this effect is of the order of 5%. (2) The deviatoric stress, or stress difference P, which leads to anisotropic velocity changes of order P/μ; these depend both on the direction of propagation and the polarization of the waves. This phenomenon is only likely to be important for seismic theory under conditions approaching internal instability and buckling.