It is most proper and basically sound to use the characteristics of inelasticity for a criterional rating of the fatigue strength of metals. This has been confirmed by much experimental data which agrees with some of the existing criteria both for low and for high loading frequencies [I]. Of all of the criteria of fatigue failure of materials the ones most accurately reflecting the physical nature of the process are those which assume that the "safe" portion of the irreversibly dispersed energy increases with an increase in the stresses [2, 3]. In this article it will be shown that we may draw this conclusion from an investigation of the laws governing the changes in the characteristics of inelasticity as a function of the amplitude of the stresses and the number of load cycles.