Irrigation systems for irrigated agriculture begin with reservoirs and basins. The latter are formed with earth dams and levees. The reliability and stability of earth dams under static and especially dynamic loading is of paramount importance. Destruction of dam structures, reservoirs, can lead to disastrous environmental and economic losses. The methods and ways to ensure the reliability of earth dams are different. Under static (own weight, water pressure) and dynamic (vibrations, explosions, earthquakes) loads, the strength and stability of earth dams are calculated at the stages of their design. In this case, it is necessary to determine the failure surfaces (surfaces of possible collapse) of the dam slopes. The circular cylindrical method for finding the failure surface (surfaces of collapse) of slopes of a homogeneous earth dam under static (own weight) loading is considered in the paper. It is shown that when the value of the total stability coefficient is greater than unity, there are local sections of the slip line where stability is violated. This circumstance creates the possibility for a fracture line development under seismic loads. It is proposed to take into account seismic stresses in the soil mass based on the solution of basic equations of continuum mechanics. The numerical solution of wave equations for the soil mass is presented by the finite difference method with known boundary conditions and zero initial conditions. The dynamic stress-strain state of earth dam is determined taking into account its moisture content and elastic, viscous, and plastic properties of soil. The ways of considering dynamic stress state when calculating the reliability and stability of earth dams are shown.