Abstract: Based on the multiple scattering theory of elastic waves, employing the wave function expansion method, the multiple scattering and the dynamic stress in semi-infinite functionally graded material with a circular cavity are investigated. The analytical solution of the problem is derived, and the numerical solution of the dynamic stress concentration factors around the cavity is presented. The effects of the distance between the cavity and the edge of the structure, the wave number and the heterogeneous parameter of materials on the dynamic stress concentration factors are analyzed. Analysis has shown that when the heterogeneous parameter of materials is less than zero, it has less influence on the maximum dynamic stress around the cavity; however, it has greater influence on the distribution of dynamic stress around the cavity. When the heterogeneous parameter of materials is greater than zero, it has greater influence on both the maximum dynamic stress and the distribution of it around the cavity, especially in the case when the distance between the cavity and the edge is comparatively small.