The authors address the problem of damage cumulation or multiple failure in the study of the process of development of a system of flaws in the form of pores or small cracks which sometimes occur during irradiation of the material by high-energy particles. To describe the process of damage cumulations, the authors use the method of similarity and express the assumption that flaw cumulation under different loading conditions is of self-similar nature. Results are submitted of the analysis of experimental data from the literature which support the assumption.