Circular lining is used widely in structure design. In this paper, the method of Green’s function is used to investigate the problem of far field solution of circular lining and linear crack impacted by incident SH-wave. Firstly, a Green’s function is constructed, which is a fundamental solution of displacement field for an elastic space possessing a circular lining while bearing out-of-plane harmonic line source force at any point; Secondly, in terms of the solution of SH-wave’s scattering by an elastic space with circular lining, anti-plane stresses which are the same in quantity but opposite in direction to those mentioned before, are loaded at the region where the linear crack is in existent actually; Finally, the expressions of displacement and stress are given when the circular lining and linear crack exist at the same time. Then, the far field of scattered wave is studied. The results can be applied in the study of fracture, and undamaged frame crack detection.