Friction forces arise at the contact between a concrete face and a rockfill dam body at deformations caused by hydrostatic pressure. They cause tensile and compressive longitudinal forces in the face which decrease the safety factor. In modern CFRD, a layer of emulsified asphalt is placed at the contact between the face and the sidewall made of low cement concrete to decrease the friction. Tests carried out in China permit determining shear characteristics of such a contact. They revealed the effect of increasing tangential stiffness with growth of compressive pressure. At high pressures the contact stiffness may reach 200÷500 MPa/m. The author refined the relationship describing the effect of increasing tangential stiffness and determined its parameters. Availability of the data on tangential stiffness and strength of the contact permitted the author to make a more precise model of the concrete face stress-strain state by the finite element method. The results of analyses showed that measures on decreasing the contact friction do not reach the required effect: considerable tensile longitudinal forces appear in the face. The contact tangential stiffness should be more decreased. Tentatively it may be recommended that in a 100m high dam to provide the face tensile strength the contact tangential stiffness should not exceed 50 MPa/m. However, for more justified conclusion it is necessary to carry out additional experimental studies of shear characteristics of the contact between face and the sidewall; and they should be conducted for conditions of very low shear rates typical for real dams.