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