Sacttering of SH-wave of combined deffectiveness which included single circular cavity and double linear cracks in elastic medium was investigated in detail. Analytic solution of this problem was obtained by Green’s Function method and idea of crack-division at actual position of crack at two times. There were two key steps of this method. First step was to employ a special Green’s Function which was a fundamental solution of displacement field for an elastic space with a cavity in it subjected to out-of-plane harmonic line source force at any point at first. The sceond step was crack-division which was artificially to produce a crack by apllying opposite shear stress caused by incident SH-wave. Distribution of dynamic stress concentration factor (DSCF) at edge of cavity was studied by numerical analysis. Distribution Curves of DSCF of three models were plotted by numerical method in polar coordinate system. Three models were one circular cavity and without crack, one circular cavity and single crack and single circular cavity double cracks. The results were compared and discussed in different incident angle of SH-wave.Conclusion was that the interaction among SH-wave, single cavity and double crack was obvious. Dynamic stress concentration factor varied with angle and distance between cavity and crack.