Scattering of SH wave by an elastic half space with a lining structure and a crack in any position and direction is studied with Green’s function, complex function and multi-polar coordinate method. First, a suitable Green’s function is constructed, which is a fundamental solution to the displacement field for the elastic space possessing circular lining structure while bearing out-of-plane harmonic line source load at arbitrary point. Then a crack in any position and direction is constructed by means of crack-division in half space. Finally the displacement field and stress field are established in the case of coexistence of circular lining structure and crack, and the expression of dynamic stress intensity factor (DSIF) at the tip of crack is given. According to numerical examples, the influences of different parameters on DSIF are discussed.