The problem of dynamic stress concentration around a shallow cylindrical cavity incident by steady-state shear horizontal SH wave in an anisotropically elastic half-space ware solved; and the rules that anisotropy of the medium influenced dynamic stress concentration around the cavity were investigated. By using the function of complex variable and multi-polar coordinate system

we constructed scattering wave function of the cylindrical cavity

which automatically satisfied the zero-stress boundary condition on the horizontal surface in elastic half-space and the Sommerfeld radiation condition at infinity. According to zero-stress boundary condition of the cylindrical cavity

we solved coefficients of the scattering wave function by least square method. Finally

the effects of different media characteristics

wave numbers

and embedded depth on dynamic stress concentration factors around the cylindrical cavity were analyzed

when SH wave incident with different angles. Numerical results show that: the dynamic stress concentration factor around cylindrical cavity increases obviously in anisotropically elastic half-space in contrast with isotropic one.