Bent circular shafts with holes in the plane of bending are of frequent occurrence in modern machines. They often form a part of the lubricating system as, for example, in the crankshafts of aircraft engines. Considerable work has been done to determine the maximum stresses and the factors of stress concentration in such shafts. The author presents a simple method of calculating such stresses for transverse holes in pure bending. Experimental photoelastic evidence that led to this method is given. A comparison of the stress-concentration factors obtained by it is made with the published results from fatigue tests and strain measurements from large steel shafts, which were performed a number of years ago at the Westinghouse Research Laboratories.