In fracture problems, stress intensity factors obtained theoretically and experimentally have been effectively utilized in the analytical evolution of the cracks effect. The effect of surface crack of a cylindrical and a hollow cylindrical bar is investigated, as well as the effect of the thickness of a hollow cylindrical bar and inclined crack of a hollow cylinder subjected to torsion moment. In this study, stress intensity factor Km of mode III which expresses the stress state in the neighborhood of a crack tip is used. stress analysis was conducted on the inside of hollow cylinder inthe axial direction of three dimensional crack tip subjected to torsion moment by combining the caustics method and the stress freezing method.