Based on the complex function method and a multipolar coordinate system, scattering of shear waves by a cylindrical inclusion in an anisotropic (orthotropic) half space is studied. In order to find the solution of shear waves, the governing equation is transferred into its normalized form. Then, the scattering wave in the half space and the standing wave in the inclusion are deduced. Different incident wave angles and anisotropies are considered to obtain the reflected wave. Then, the unknown coefficients in scattering wave and standing wave are found by utilizing the continuous condition at the boundary of the inclusion. Subsequently, the dynamic stress concentration factor (DSCF) around the inclusion is calculated and analyzed. The results demonstrate that the distribution of the DSCF is influenced by the anisotropy of the half space, and the value of the DSCF is mainly affected by the wave numbers ratio and the shear modulus ratio.