Results are considered of systematic study of stress-strain state (SSS) of a seepagecontrol wall arranged in the embankment dam foundation. The following factors affecting the wall SSS were studied: the wall depth, deformation modulus of the wall material, the pattern of the wall resting. Studies were conducted with the aid of numerical modeling. They revealed significant role of friction processes and slippage at the contact with soil on the wall SSS formation. It is friction through which soil transfers to the wall the compressive longitudinal forces which increase while the wall stiffness increases. It was also revealed that conditions of operation of suspended walls are more favorable that those of walls resting on rock. Empirical formulae were proposed which permit predicting the value of maximum compressive forces in the wall. Compressive strength of the wall was assessed. At that, it was taken into account that strength of plastic clay-cement concrete considerably increases if it is compressed from all sides as compared to uniaxial compression. A considerable role of accounting this effect was shown at selecting material for arrangement of the wall. It was obtained that to provide the wall strength it is necessary to have its material deformability exceeding the deformability of the surrounding soil not more than 5 fold. It was revealed that at perceiving by the wall the horizontal forces of seepage or hydrostatic pressure the longitudinal forces in it sharply decrease. It was obtained that then there is a danger of the wall tensile stress failure, because bend deformations in the wall cause irregular distribution of stresses in it. Especially it is hazardous for the walls made of rigid materials.