This paper is concerned with the torsional impact response of an infinite body with two annular cracks. The method of analysis is the body force method extended to elastodynamic problems, which was developed previously by the anthors. In this method, the solutions are obtained by superposing the elasto-dynamic stress fields of point force so as to satisfy the given boundary conditions. The dynamic stress intensity factors are obtained numerically, and the effects of the interactions between two cracks on the dynamic stress intensity factor are shown graphically.