An analysis of shear characteristics on the concrete–rock mass interface is presented, in order to simulate the effect of load at the contact of concrete structure of the dam and the rock foundation. The analysis is based on the real mechanism of shear, which is different from the so-called the “saw tooth” model that simulate the walls of joints in the rock mass. As a result, the analytic form of shear deformation and shear strength as a function of normal and shear loads, as well as the mechanical characteristics of the rock mass, is established. In this way, mathematical models are derived that can be used for structural analysis of Concrete Dams for the Preliminary Design level. The models are developed on the basis of a large number of shear tests carried out on the concrete blocks at the concrete dam sites, during the period from the seventies to the present day.