This paper presents a study of yield points of mild steel which utilized solid and hollow cylinders with a transverse hole under torsion. The maximum tensile stress was found at an intersection of hole and outer surface of the cylinder by observing the torsional fracture face of polymethly methacrylate (PMMA). This analysis has been carried out with the surface layer theory applied to the maximum shear stress which occurred at the edge of the hole in an infinite plate subjected to pure shear. The analytical results coincided well with the experimental data in the following points. (1) Yield points of cylinders depend only on hole diameter and are free from the influence of the outer diameter and the ratio of inner to outer diameter of cylinders. (2) There are two kinds of yield points with respect to the diameter of the hole. In the case of a hole with a comparatively small diameter, the yield point is independent of the hole diameter of the cylinder.