In this paper we studied the influence of the initial stress on the propagation of Rayleigh waves in a homogeneous-isotropic, generalized thermo-elastic body, subject to the boundary conditions that the outer surface is traction free. In addition it is subject to linear radiations, adiabatic isothermal transfer conditions. We found that the frequency equation of Rayleigh waves contains a term involving the initial stress and, therefore, the phase velocity of Rayleigh waves changes with respect of this initial stress, when the initial stress, vanishes, the derived frequency equation reduces to that one obtained in classical generalized thermo-elastic case which includes the relaxation time of heat conduction.