<p>In this paper, the dynamic problem of a circular cavity in an elastic half-space with initial stress is studied. Firstly, the equilibrium equation for the two-dimensional elastic medium with initial stress under the SH wave is obtained by tensor analysis. Then, the analytical expression of scattering wave is established by conformal mapping method and substitution method. Finally, based on the theory of incremental elasticity, the expression for the total stress is derived. The integral equations are set up through boundary conditions and solved by applying orthogonal function expansion technique and effective truncation. The calculation results analyzed and discussed the dynamic stress concentration factor around the circular cavity. Besides, the analytical solutions are compared with the finite element solutions to verify the accuracy of the conclusions in this article.</p>