The deformed and strength state of earthen dams in narrow valleys during earthquakes differs from solutions in the plane statement. This difference is associated with variation in the dynamic properties of the dam, its shape, and natural-vibration frequencies, and with the effects of hang-up of the diaphragm on the rock edges, etc. This paper cites examples of solution of the plane and three-dimensional problems for a 100-m-high earthen dam with a bituminous-concrete diaphragm in a narrow valley subject to 9-point earthquakes.Keywords: seismic effect, residual displacements in dams during earthquakes, stress state of dam, strength state of soil, spread velocity of seismic waves, earthquake resistance of dams, crack formation in core, contact filtration.The earthquake resistance of gravity dams during earthquakes is evaluated on the basis of assigned strength and stability criteria. For earthen structures possessing their own strength state under load, the strength criterion may be the "reliability index" [1]. This quantity defines the ratio of the energy of bulk compression associated with consolidation of the soil to the energy of shear deformations, an increase in which will lead to disturbance of soil stability and development of plastic deformations.Values of plastic deformations that are acquired during an earthquake and define residual displacements within the dam, its settlements, and movements are used as stability criteria for analysis of earthen dams.In addition, the maximum dynamic accelerations manifested within the dam during an earthquake are no less important for evaluation of earthquake resistance of the dams. The values of the dynamic accelerations determine the values of the inertial loads and dynamic stresses. It is precisely these stresses that frequently determine the conditions of the structure's normal behavior. In the surface zones of the dam, where compressive stresses due to its own weight are high, dynamic stress pulsations may lead to appearance of zones of soil loosening, and, consequently, to manifestation of cracks on the crest, and disturbance of the soil's stability in the near-slope zones. In regions where a local stress reduction during static functioning of the dam, for example, due to the "arch effect," dynamic-stress pulsations may cause loosening of the transition zones and zones of contact on the boundary with the edge abutments. The most dangerous consequences of alternating-pulsating stresses may be cracks induced by hydraulic rupture in the core of the dam and formation of concentrated filtration paths on the boundary with the rock edges.A large number of both design and analytical factors, the most significant of which are described below, will affect the stress-strain state (SSS) of the dam during earthquakeinduced effects.Consideration of spatial characteristics of dam behavior. When dams in broad valleys are analyzed, it is accepted to consider that the effect of the three-dimensional character is close to zero, and the design scheme can be simplified to conditions o...