This article deals with the development of a new high-strength construction of a slide protective earth dam, which is based on the use of conventional local geomaterials such as soils, sand, stones, crushed stone, various kinds of crushed rocks etc., in combination with geosynthetic materials erected by inclined layers. The study describes the technology of construction of trapezoidal in the cross section of the earth dam with horizontal and inclined layers of geosynthetics and algorithms of the developed computational mechanical and mathematical model of the study of stress-strain state (SSS). Some steps of the algorithm of the finite element method and the results of the study of the SSS section of the earth dam for different angles of the inclined layers are presented. The analysis of the results obtained by multivariate calculations are presented in the form of strain and stress diagrams. It is concluded that in the construction of the dam inclined layers with angles φ from 0 to 900 with their gradual growth, the deformation values are reduced inversely, which means that the dam will become more stable in comparison with the construction of traditional horizontal layers.