Mathematical statement, methods and algorithms of assessment of stress-strain state of earth dams with account of elastic-plastic, moist properties of soil and finite strain, structural heterogeneity of structures under static effects, are presented in the paper. Stress-strain state of three erected structurally heterogeneous earth dams of different heights was studied with account of elastic-plastic, moist properties of soil and large strains in a structure. In the process of investigation it was revealed, that an account of elastic-plastic properties and moisture content of soil, as well as large strains and heterogeneity of a structure, qualitatively and quantitatively vary the state of high earth dams, increasing arch effect for vertical stresses and horizontal stresses in the base of a dam, changing stress state of a structure on the whole and bringing the drop in pressure on the contacts of different parts of a structure.