Abstract: The solution to the dynamic stress concentration of circular cavities and inclusions subject to SH-Wave in an elastic half-space covered with an elastic layer is attained in this study, using the complex function method and the wave function expansion method. According to the attenuation characteristics of SH-Wave scattering, the problem is attempted by using the large-arc assumption method, in which a circular boundary of a large radius is used to approximate the straight boundary of the surface layer to transform the original problem to a surface boundary problem. With the theory of Helmholtz, the general solution of the Biot’s wave function is obtained. Subsequently, infinite linear algebraic equations with unknown coefficients are formulated using the Fourier-Hankel series expansion and boundary conditions, and the approximate analytic solution is derived by truncating the equations. Finally, the dynamic stress concentration factor around the circular inclusion is discussed in a numerical example. Results show that different stiffness and thickness of the surface layer and the existence of cavities can remarkably change the dynamic stress concentration distribution around circular inclusions.