Propagation of the generalized Rayleigh waves in an initially stressed elastic half-space covered by an elastic layer is investigated. It is assumed that the initial stresses are caused by the uniformly distributed normal compressional forces acting on the face surface of the covering layer. Two different cases where the compressional forces are "dead" and "follower" forces are considered. Three-dimensional linearized theory of elastic waves in initially stressed bodies in plane-strain state is employed and the elasticity relations of the materials of the constituents are described through the Murnaghan potential where the influence of the third order elastic constants is taken into consideration. The dispersion equation is derived and an algorithm is developed for numerical solution to this equation. Numerical results for the dispersion of the generalized Rayleigh waves on the influence of the initial stresses and on the influence of the character of the external compressional forces are presented and discussed. These investigations provide some theoretical foundations for study of the near-surface waves propagating in layered mechanical systems with a liquid upper layer, study of the structure of the soil of the bottom of the oceans or of the seas and study of the behavior of seismic surface waves propagating under the bottom of the oceans.