Within the framework of the piecewise homogeneous body model with the use of the three-dimensional linearized theory of elasticity the influence of the third order elastic constants on the velocity of the generalized Rayleigh wave propagation in a pre-stressed stratified half-plane is investigated. Between the layer and half-plane the complete contact conditions are satisfied. The concrete numerical investigations are made on the various materials for which the values of the third order elastic constants are known. The initial stresses are determined within the framework of the classical linear theory of elasticity. (C) 2003 Elsevier Ltd. All rights reserved.