The Green’s function of a right-angle plane including semi-cylindrical canyon while bearing out-of-plane harmonic line source load on horizontal interface have been considered using the methods of complex function and image. Firstly, the wave field of right-angle plane was imaged half space, the scattering wave field, which satisfies the free stress boundary conditions of the right-angle plane on the vertical interface could be constructed. Secondly, a series of infinite algebraic equations be obtained to settle this problem by considering the stress free boundary condition of semi-cylindrical canyon. Finally, some examples for ground motion of a right-angle plane were given and discussed. Numerical results show that displacement of the horizontal surface is influenced by right-angle free boundary.