Deterministic method of analysis of the combined strength of parts, with external and internal parameters being random, has been proposed. In this procedure the deterministic functions and values computing the random parameters influencing on the parts strength have been used. In this procedure the deterministic functions and values computing the random parameters influencing on the parts strength have been used. The method for constructing approximate solutions of the stochastic

elasticity problem has been given. It has been showed that for part with random parameters exist crowd equivalent strength conditions. It has been proved that equally stressed structures have smaller safety factor and service life rather than structures with stress concentrators under otherwise equal conditions.

Key word: elastic parts, generalized equivalent stresses, stochastic elasticity problem, safety factor, equivalent strength conditions, service life.