ABSTRACT. Simultaneous nonlinear propagation of two longitudinal waves in opposite directions in an inhomogeneously predeformed elastic medium is investigated theoretically. The method for nondestructive characterization of a predeformed medium is proposed. The method basis on the wave induced stress measurement data on two opposite surfaces of the medium. The utilization of the method is illustrated by sine-waves propagation in physically nonlinear elastic medium undergoing plane strain. The nonlinear distortion of sine-waves profiles due to propagation, reflection and interaction in predeformed medium is studied in detail. The dependence of nonlinear wave profile distortion on the parameters of the predeformed state is clarified.