The scattering of plane SH-waves by topographic features in a layered transversely isotropic(TI) half-space is investigated by using an indirect boundary element method(IBEM).Firstly, the anti-plane dynamic stiffness matrix of the layered TI half-space is established and the free fields are solved by using the direct stiffness method.Then, Green’s functions are derived for uniformly distributed loads acting on an inclined line in a layered TI half-space and the scattered fields are constructed with the deduced Green’s functions.Finally, the free fields are added to the scattered ones to obtain the global dynamic responses.The method is verified by comparing results with the published isotropic ones.Both the steady-state and transient dynamic responses are evaluated and discussed.Numerical results in the frequency domain show that surface motions for the TI media can be significantly different from those for the isotropic case, which are strongly dependent on the anisotropy property, incident angle and incident frequency.Results in the time domain show that the material anisotropy has important effects on the maximum duration and maximum amplitudes of the time histories. The scattering of plane SH-waves by topographic features in a layered transversely isotropic (TI) half-space is investigated by using an indirect boundary element method (IBEM). Firstly, the anti-plane dynamic stiffness matrix of the layered TI half-space is established and the free fields are solved by using the direct stiffness method. Chen, Green’s functions are derived distributed uniformly acting on an inclined line in a layered TI half-space and the scattered fields are constructed with the deduced Green’s functions. Finally , the free fields are added to the scattered ones to obtain the global dynamic responses. The method is verified by comparing results with the published isotropic ones. Both the steady-state and transient dynamic responses are evaluated and discussed. Numerical results in the frequency domain show that surface motions for the TI media can be significantly different from those for the isotropic case, which are strongly dependent on the anisotropy property, in cident angle and incident frequency. Results in the time domain show that the material anisotropy has important effects on the maximum duration and maximum amplitudes of the time histories.