Abstract: Based on the mechanics of anisotropic materials, the dynamic propagation problem of a mode III crack in an infinite anisotropic body is investigated. Stress, strain and displacement around the crack tip are expressed as an analytical complex function, which can be represented in power series. Constant coefficients of series are determined by boundary conditions. Expressions of dynamic stress intensity factors for a mode III crack are obtained. Components of dynamic stress, dynamic strain and dynamic displacement around the crack tip are derived. Crack propagation characteristics are represented by the mechanical properties of the anisotropic materials, i.e., crack propagation velocity M and the parameter α. The faster the crack velocity is, the greater the maximums of stress components and dynamic displacement components around the crack tip are. In particular, the parameter α affects stress and dynamic displacement around the crack tip.