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Abstract.A relaxation of stress in the elements of constructions is considered and an approach is proposed for solution of corresponding problems. It is notable that this approach is based on a modification Boltzmann's principle superposition of fraction creep deformations. This modification reduces the noted problems to solution of linear relative to socalled structural stress integral equations. Next a desired stress is defined by solution of algebraic equations. It should be underline that a material (concrete, steel, graph) of elements a considered as a union of its fractions with statistical disturbed strengths. This ascending to Weibull conception [1] permits to modify Boltzmann's principle superposition [2]. As a result this principle is applicable when a dependence on deformations from the stresses is nonlinear [3][4][5][6][7].According to Berg [6] and Gvozdev [9] an increasing on cross-section loading N W implies destruction a certain fractions of the element. Here W is a current temp. In consequence of this destruction an initial areais called the structural stress. Sinceis the normal stress then according to the relations (1) and (2)

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Aims of research. Derivation of consistent equations of the theory of thin elastic shells without hypotheses and stress averaging over the shell thickness. Methods. Using the iterative method of Saint-Venant - Picard - Banach, the three-dimensional problem of the theory of elasticity is solved without any hypotheses. By the principle of compressed mappings, the solution converges asymptotically, regardless of the choice of the values of the initial approximation. Results. A method has been developed for integrating the spatial equations of the theory of elasticity in curvilinear coordinates for a thin shell. The presence of a small parameter allows the integration of the system of equations in such a way that the output data of the first operator is input to the next operator, etc., dividing the original complex operator into a sequence of simple integrable Picard type operators. Each equation contains terms of only one asymptotic order.