The responses of transient SH waves propagating in a double dipping layered medium overlaying half‐space are investigated in this study. To obtain the responses, a line source, with a parabolic ramp and a triangular time function is assumed to be located in the top dipping layered medium. Then the generalized ray theory and Cagniard method [13], were employed to solve the problems of the first and second wave trains respectively. Finally, the ray paths and responses for the distinct locations on the surface are obtained and are shown in the sketches. As for the total responses, it is found that the consideration of the responses for the second wave train in far field is more important than in near field.