<p>Since composite materials play an important role in many fields, mechanical properties of different composite materials need to be paid attention. Put an eye on the mechanical properties of different kinds of materials, influences on stresses between varies media with inhomogeneity or anisotropy are needed to be investigated. In this paper, scattering by a cylindrical inclusion under shear horizontally (SH) wave incidence is analyzed. The background medium is inhomogeneous while the embedded inclusion is orthotropic. In order to model the two dimensionally graded inhomogeneous medium, the density of the medium is described by a function in polynomial form. Hence, partial differential equations of wave motion in background medium and the inclusion are established and the complex function method is applied to solve the wave equation. Analytical expressions of displacements and stresses in inhomogeneous medium and the inclusion are formulated and the undetermined coefficients are solved by utilizing boundary conditions. Dynamic stress concentration factor (DSCF) at the interface of the inclusion and the DSCF nephogram around the inclusion are calculated and visualized. Typical results implies the value of DSCF is mainly effected by the inhomogeneous parameters and shear modulus ratio, it is effected by the orthotropy of the inclusion as well.</p>