The aim of the paper was to review the stress-strain state of an arch-gravity dam of the SayanoShushenskaya HPP, which has construction and contact joints. The problem is solved by finite element method using software package SOFiSTiK. The finite element model of the "dam – foundation – abutments" created at the department "Structural mechanics and theory of elasticity" of SPbSPU is described. Three-dimensional 8-nodal finite elements were used. Joints in the dam body were modeled by unilateral constraints. The schemes of unilateral constraints location in contact and construction joints are presented. To assess the correctness of the finite element model operation the calculated radial movements at the crest of the dam was compared with the field data. Satisfactory agreement of values confirms the correctness of modeling system behavior by the design scheme. According to the calculation results from the action of the hydraulic load we can conclude that account of the disclosure joints leads to a significant increase in the calculated stresses in the dam body.