The strength theory of Coulomb-Mohr in its traditional understanding is true only for the conditions of free dilatancy and the critical initial density of composition of grainy medium. This peculiarity is the main reason of failures when employing it for solving a number of tasks facing modern geotechnics. In order to adjust the conditions of strength to the conditions of constrained dilatancy, it is necessary to introduce two principal amendments. First, Normal pressures in the process of failure of grainy medium are not constant, but depend on the reaction of the surrounding massif to the accompanying volume deformations. Second, the angle of internal (contact) friction depends on the degree of realization of the angle of grain gear, which is determined by the conditions of development of dilatancy.