<p>The experimental investigations of the mechanical behavior of complex structures are fairly restricted and extremely expensive. At the same time, the application of simplified mathematical models for the evaluation of the strength characteristics and service life of these structures may lead to significant errors. Therefore, the analysis of the mechanical behavior of complex structurally inhomogeneous structures of rocket engineering aimed at the evaluation of their failure loads are more and more often carried out on the basis of the refined mathematical models capable of taking into account both the complex shape of structures and the nonlinear behavior of materials. We propose a refined mathematical model for the evaluation of failure loads under the assumption that displacements and strains are significant and the stresses noticeably exceed the plasticity limit of the materials. The problem is formulated within the framework of geometrically nonlinear elastoplasticity. To solve the problem, we use the finite-element method. On this basis, we study the stress-strain state of a fuel-compartment tank of the rocket under the conditions corresponding to the destructive tests of the tank. The obtained values of the failure loads and the sites of occurrence of the maximum stresses in the tank are in good agreement with the data of full-scale destructive testing. The proposed methodology makes it possible to significantly decrease the number of full-scale experiments in the course of which the structures are destroyed.</p>