It is assumed that the cyclic strength is defined by the value of latent energy which is considered as the damage parameter. This parameter is governed by the differential equation with the solution in the form of the logistic function, capable to describe different processes leading to saturation. The functions and parameters of the received criterion are concretized and comparisons with the experimental results for axial cyclic tension for sheet aluminum alloy specimens are given. A good agreement of theoretical and experimental results is received.