For the efficient error control of numerical solutions of the solid mechanics problems, the two requirements are important: an a posteriori error bound has sufficient accuracy and computation of the bound is cheap in respect to the arithmetic work. The first requirement can be formulated in a more specific form of consistency of an a posteriori bound, assuming that it is not improvable in the order and, at least, coincides in the order with the a priori error estimate. Several new a posteriori error bounds are presented, which improve accuracy and reduce the computational cost. Also for the first time a new consistent guaranteed a posteriori error bound is suggested.