The influence of the third order elastic constants on the dynamical (time-harmonic) axisymmetric interface stress field in the system which comprises the half-space and the pre-stretched covering layer is investigated within the framework of the piecewise homogeneous body model by employing the three-dimensional linearized theory of elastic waves in initially stressed bodies. The elasticity relations for the layer and half-space materials are given through the Murnaghan potential. It is assumed that the force acting on the free face plane of the covering layer is a time-harmonic point-located normal force. The influences due to both of the quantities of the pre-stretching of the layer and the third order elastic constants of the layer material on the interface normal stress are analysed. The numerical results are presented for concrete selected materials such as steel, aluminium, and acrylic plastic. (c) 2005 Elsevier Ltd. All tights reserved.