Ensuring the safety of hydraulic structures should be carried out, including calculations of the stress-strain state of the system "structure-base" by the method of limit States. A summary system of reliability coefficients, a combination of loads and operating conditions for different design cases is presented. Considered the stability condition of the concrete dam on the shift on the substrate. A comparison of the values of the generalized dam stability coefficients (reserve) according to Russian norms and American standards is performed. It is shown that when comparing the numerical values of the strength and stability coefficients regulated in the Russian norms and American standards, it is necessary to take into account the methods of determining the strength characteristics of materials, the practice of taking into account loads and effects, as well as the methods of computational studies of the stress-strain state of structures and their bases.