The increase in the requirements on the reliability of units makes it necessary to analyze the relationship between mathematicalmeth ods of calculating reliability and the physical nature of fail ures. The difficulty of such an analysis is obvious. On the one hand, in making a representation of the physical picture of a phe nomenon, one can make an error in the direction of excessive sim plification. On the other hand, in the mathematical treatment of the physical scheme, it may be necessary to use extremely complex and fine analytical methods, and their simplified exposition bor ders on vulgarization. Without the aid of a large number of specialists working in the field of analysis and calculation of systems reliability, an ex posi tion of models of failures and their mathematical treatment would be unobtainable. The authors take this opportunity to express their gratitude to Academicians N. G. B r u y vic e h and Y u. V. Lin n i k conversations with whom clarified a number of problems treated, to active member of the Academy of Sciences of the UkrSSR B. V.