The far field solution of SH-wave by arbitrary shape cavity on the interface is investigated by the methods of Green’s function and complex function. A suitable Green’s function is constructed, which is the fundamental solution of displacement field for an elastic half space with any canyon under anti-plane harmonic line source loading at an arbitrary point on the horizontal surface．And the model of scattering of SH-wave by a cavity, which is on the interface of two different media, can be built based on the idea of conjunction. Then a series of Fredholm integral equations of the first kind for determining the displacement mode of scattered wave at far field and scattering cross-section can be set up through the Green’s function. The numerical examples are given and the far-field characteristics of SH wave scattering by elliptical and quadrate cavity with different media combination are discussed.