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General information on aftermath, behavior and damage analysis of earth dams under severe earthquakes is given in the monograph. Different models of soil are analyzed and the possibility of the use of hereditary model of viscous-elasticity for the description of rheological and dissipative properties of soil is shown. Mathematical statement and the methods of solution of the problems for earth dams with account of linear and non-linear elastic, viscous-elastic, elastic-plastic and water saturation properties of soil are considered with account of finite strain under different static and dynamic effects using plane, cross and spatial models of the structure. Criteria for the assessment of strength reliability of earth dams are given. The monograph is intended for the masters, post-graduate students, scientific researchers and specialists who work in the field of mechanics of deformable rigid body, structural mechanics, hydro-technical and seismic engineering; it may be helpful forengineers and designers who work in projecting and engineering of hydro-technical structures of soil material.