In this paper, it is shown that mixed FEM problems in elasticity theory, if polynomials of the same order are used to interpolate displacements and stresses, and if the stress boundary conditions x are satisfied as essential, as a rule do not satisfy the Brezzi conditions. The problem can be solved formally if we take higher-order interpolation functions for stresses. The details of the solvability of this problem are analyzed. Special attention is devoted to some quantitative characteristics (dimensions) of the considered subspaces of finite elements. Superconvergent numerical solutions justify the proposed calculation scheme.