The object of the present paper is to investigate the influence of initial stress on the waves propagation in a generalized thermoelastic granular medium subjected to the boundary conditions that the outer surface is traction free. In addition, it is subjected to temperature boundary conditions. The wave velocity equation for the generalized thermoelastic granular medium Rayleigh wave under the influence of initial stress has been obtained. The classical result has been derived as a limiting case similar to one which was obtained by Ewinget al. (1957).