An issue of dynamic stress concentration for shallow buried circular cavity in a soft layered half-space under steady SH-Wave has been studied based on complex function and wave function expansion method, and analytical solution is obtained. According to the attenuation characteristic of SH-Wave scattering, using large-arc assumption method, that is, straight boundary of the surface layer is approximated by a circle with large radius, which lead to a surface boundary problem. Firstly, the general forms of unknown wave function are given on the basis of Helmholtz theorem. Then, according to the boundary conditions and the complex Fourier-Hankel series expansion method, the problem is transformed into the infinite linear algebraic equations of the unknown coefficients in the solution of the wave function. From the finite terms, the numerical results can be obtained. The sample analyze the influence on distribution of dynamic stress concentration factor around shallow buried circular cavity in a soft layered half- space when SH-Wave is normal incidence, including the wave number difference between overburden layer and half space medium in different incident frequency, the variation on the cover thickness and the buried depth of the circular cavity.
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