Abstract: The scattering of SH-wave by a bi-material interface crack and a neighbouring circular cavity in vertical half-space are studied based on the image method. Firstly, a suitable Green’s function is constructed in right-angle plane. Secondly, the methods of ‘interface conjunction’ and crack-division are used to construct the scattering model of SH-wave. The Bi-material media is divided into two right-angle planes along the horizontal interface, and horizontal surfaces are loaded with undetermined anti-plane forces in order to satisfy continuity conditions at the linking section, with some reverse forces to produce cracks by means of crack-division technique. Then the problem is converted into the solution of Fredholm integral equations of first kind by means of the Green’s function. Finally, using the attenuation speciality of SH-wave, the integral equations can be dispersed to linear equations directly, so the numerical solution can be obtained. The dynamic stress concentration factors around the circular cavity are discussed. The calculating results show that the existence of free boundary of vertical half-space has great effects on the dynamic stress concentration factors. Moreover, the existence of interface crack has also great effects on the dynamic stress concentration factors around the circular cavity.