The study is devoted to the stress-strain state (SSS) of various earth dams analyzed using a spatial model. The article provides a detailed review of well-known scientific publications on the SSS assessment of dams. In this article, a mathematical model was developed to assess the SSS of earth dams using a spatial model based on the Lagrange variational equation, considering real geometry, properties of the material, and non-homogeneous design features of structures. A technique was developed for solving spatial problems to assess the SSS of earth dams by the finite element method using the program developed by the authors and the ABAQUS software. The adequacy of the mathematical model and the accuracy of the results obtained were verified by solving test problems. The SSS of the Ghissarak (H = 138.5 m), Sokh (H = 87.3 m), and Pachkamar (H = 70.0 m) earth dams under the action of body forces and hydrostatic water pressure was studied. It was established that the greatest displacements were observed on the crest and in the zone of the dam core; an account for nonhomogeneous design features significantly affects the resulting displacement field in the core zone; a spatial deformed state of the structure occurs near the banks; positive stress (not considered in a plane model) arises in a small area in the upper part of the core near the crest, caused by the crest indentation by the lateral surcharge.