Strength assessment of earth dams is mainly conducted using a plane design scheme, which does not always lead to adequate results. In this paper, it is proposed to assess the stress state of earth dams in a three-dimensional statement. Consequently, to assess the stress-strain state and dynamic characteristics of earth dams, appropriate mathematical models, methods and algorithms are built. The basis of the developed methods for solving specific problems for a spatial structure is a finite element method, the Gauss method (or the square root method) and the Muller method. Reliability of results is proved by solving a series of test problems. With the developed methods, the stress-strain state and dynamic characteristics of the Gissarak and Sokh earth dams were investigated. Based on the results of the study, it has been shown that for some types of earth dams, at preliminary assessment of the stress state and dynamic characteristics of structures, it is possible to use a plane-deformable model of calculation. Studies have shown that to ensure the required accuracy in assessing the stress state and dynamic characteristics of complex inhomogeneous spatial systems (such as earth dams), it is necessary to make calculations using a three-dimensional model. The data obtained as a result of research allowed to reveal some features of the stress state in a spatial case, indicating dangerous areas with the greatest stresses, as well as to study the pattern of natural oscillations that cannot be described using a plane model.