Considering properties of materials can not abruptly change, an interface layer model with the linear continuous transitive properties is proposed for the double half planes to investigate the problems of SH waves propagation in the double half planes with the interface layer taken into account, the reflective and refractive waves would exhibit phase shifts. The amplitudes of the phase shifts of the reflective and refractive waves vary greatly with the thickness of the interface layer, properties of media and incident angle. It suggests that there is probably considerable errors in understanding the problems of wave propagation under conditions of neglecting the interface layer structures.
