In this paper the torsion of shafts with transverse holes has been investigated experimentally. Usual methods for stress measurements, such as the method of brittle coatings and the use of sensitive extensometers, are not applied effectively to the present problem because the maximum stress occurs in the bore and does not occur on the outer surface of the shaft. The stress may be measured by the stress-freezing and slicing method but we cannot expect too much from this method for the accurate determination of the stress when the diameter of the hole is comparatively small. In treating the problem theoretically, considerable mathematical difficulties are encountered on account of its axially nonsymmetrical nature. The electroplating method recently developed by one of the authors (1), however, has been proved to be useful in this case, so the maximum stresses in shafts are measured by this method and the stress-concentration factors are found for various diameters of the hole.