The torsion problem of a bar with varying circular section has been treated by several investigators over a long period. Usually, the solution covering all points in a shaft is found first and then the maximum stress is obtained. Accordingly, the analysis usually becomes complicated and so only few cases have been treated completely. It is essential from the technical point of view, however, to find the stresses around a notch rather than the stresses at every point in a shaft. The approach employed in this paper is somewhat different from others, and the approximate values for the stresses on the surface of a shaft are found directly without solving the problem completely.