Abstract: In this paper, the scatting of SH-wave by asemi-cylindrical hill above a subsurface cavity in half-space is studiedbased on the idea of match up, by using complex functions andmulti-polar coordinates. During the solution, we divide the solutiondomain into two. Thefirst one is a circle domain, including the boundary of the hill, andthe second one consists ofall of the rest parts. A solution is constructedin the circle domain, where satisfies the condition that stress is zero atthe hill edge and arbitrary at the other part. In the second domain, including asemi-cylindrical canyon and a subsurface cavity in the half-space,the scattered wave function is constructed, which satisfies the condition of stress free atthe horizontal surface. Then, by using the moving coordinate method, thetwo solutions are matched up on the junction interface, satisfying the boundary conditionat the subsurface cavity edge. The problem can be reduced tosolve a set of infinite linear algebraic equations. Finally thecomputational results of surface displacement are presented togetherwitha discussion.