SUMMARYEquilibrated solutions, locally satisfying all the equilibrium conditions, may be obtained by using a special case of the hybrid finite element formulation. Unlike simplicial super-elements in 2D and 3D, which are free from spurious kinematic modes, and the quadrilateral super-element with diagonal subdivision, which has exactly one internal spurious kinematic mode, no hexahedral super-element free of external spurious kinematic modes is yet known as far as the author is aware.