Many machine members, such as shafts and axles, are subjected to stresses which do not remain constant in magnitude but fluctuate with time. Under such conditions, the resisting strength of the material is reduced and hence a different working stress from that for static stresses must be used. To determine this working stress, it is convenient to first establish the maximum working stress for simple tension in the case of fluctuating stress. With this as a basis, the case of combined stresses can then be considered. The evaluation of working stresses for members subjected to fluctuating combined stress has been made by Soderberg, based on a shear theory of failure. However, recent tests by Gough, indicate that for ductile materials, a shear-energy theory is in better agreement with experiment. The following paper deals primarily with the formulation of such a theory and its application to design. In addition, a comparison is made of designs by this theory with those now in use. In this discussion, ductile materials are considered and, in particular, medium-carbon steels.