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.