A new design formula of axles for railway rolling stock is newly given by the writers basing on the experimental results obtained by the writers and other authorities. Calculations of the factor of safety of the axles, which are used by several railway co. in Japan and of the axle failure due to fatigue under service conditions, were made. And the relation between the factors safety and the actual lives until the axles failured were studied. In the light of the studies, it becomes clear that the axle, the factor of safety of which is 1 as calculated with the new formula, has a life above 15 years, and that the new formula is correct to discuss the fatigue strength of axle and its life.