The article provides a detailed review of well-known publications devoted to studying the stress state and dynamic behavior of earth dams, taking into account the elastic and elastic-plastic properties of soil. To assess the stress-strain state of earth dams, considering the elastic-plastic properties of soil under the action of static loads, a mathematical model was developed using the principle of virtual displacements. A technique, algorithm, and computer programs were developed for estimating the stress state of dams using the finite element method and the method of variable elasticity parameters. A test problem was solved to assess the adequacy of the developed models and the reliability of the technique, algorithms, and computer programs. The stress-strain state of the Pskem earth dam, 195 m high, was studied using the developed models and calculation methods, taking into account the elastic-plastic properties of soil under the action of body forces and various levels of filling the reservoir with water. It was established that an account for the elastic-plastic properties of soil leads to a sharp change in the stress state of the dam, especially in the upper prism and in the core of the dam, and changes the intensity of normal stresses, which can lead to a violation of the integrity of the dam.