Abstract: Based on the complex variable method with a mapping function, an approach to solving the scattering problem of SH-waves due to an elliptical inclusion in a right-angle plane is presented in this paper. The image method is employed to construct the equal incident and reflection waves which have to satisfy the stress free condition on the straight boundaries. Then the conformal mapping method is used to map the outer boundary of elliptical inclusion onto a unit circle to construct the expression of scattering waves of the elliptical inclusion. Through the continuity conditions on the boundary of the inclusion, a series of integral equations that determine the unknown coefficients are set up and solved by the effective truncation method. The ground motion on the horizontal boundary is presented, and numerical results show that incident wave, incident angle, position of the inclusion, medium parameters, and so on have an effect on the ground motion.