The paper provides a detailed analysis of known publications devoted to various models and methods, as well as the results of the study of the stress state of structures, taking into account the elastoplastic properties of soil. A mathematical model, methods, and an algorithm to assess the stress-strain state of earth dams were built considering elastoplastic properties of soil, inhomogeneous structural features and the filling level of the reservoir under various influences. A variational equation of the principle of virtual displacements, and the finite element method and the method of elastic solutions were used to solve the problem. The reliability assessment of the results obtained was verified by studying the practical convergence of various model problems. The stress-strain state of three earth dams (of different heights) was investigated taking into account the elastic, elastoplastic properties of soil at different filling levels of the reservoir. At that, various mechanical effects were revealed, i.e., the appearance of additional strains in the most stressed places inside the dam body, and the occurrence of significant plastic shear strain in the slope zones and the smoothing of the arch effect in the core zone. It was found that an account of elastoplastic properties of soil at a completely filled reservoir significantly changes the pattern of shear stresses distribution in the body of the dam, i.e. they increase both in the upper retaining prism and in the lower prism.