In this paper, based on a expansion technique proposed by Yeh et al. (1995), the dynamic stress concentration of a cylindrical cavity buried in an elastic half-plane is studied. The cavity and the half-plane are excited by a harmonic standing Goodier-Bishop stress wave which, as a result of taking the normalized frequency tends to zero, is equivalent to a simple uniform static tension parallel to the ground surface. In the formulation, the scattered waves are represented by series expansion and their associated modal fields of the expansion satisfy the boundary conditions on the ground surface as well as the radiation condition at infinity, thus the scattering problem is reduced to the determination of the expansion coefficients by matching the boundary conditions on the cavity. Some numerical results for the dynamic hoop stresses around the wall of the cavity as well as the dynamic stress concentration factors with various buried depth and excitation frequencies are presented.