А model is proposed to describe the development of the damage of material. The model considers the origin of the defects in the process of cyclic action. The role of the utilized parameters is anafyzed. The model is applied to the construction of generalized longevity curves for the symmetrical and asymmetrical load cycles and dependences of "the medium stress of a cycle - amplitude o f vibrostress” for the assigned levels of longevity (Haigh's diagram). Also considered under the model is the question about the probability distribution of destruction de-pending on amplitude and load duration. Conclusion is drovvn about the adequacy of the model to the experimental data.