A rigorous treatment is given of the problem of wave propagation in an elastic continuum when the influence of the initial stress is taken into account. After a short review of the theory various cases of initial stress are considered. It is shown that a uniform hydrostatic pressure does not change the laws of propagation. A hydrostatic pressure gradient produces a buoyancy effect which causes coupling between rotational and dilatational waves. Bromwich's equations for the effect of gravity on Rayleigh waves are derived from the general theory and the physical transition from Rayleigh waves in a very rigid medium to pure gravity waves in a liquid is discussed. The case of the vertical uniform stress is also considered and it is shown that the effect of the initial stress on the waves in this case cannot be accounted for by elastic anisotropy alone. Reflections may be produced by a discontinuity in stress without discontinuity of elastic properties.