In this paper, an energy-compatibility condition is used for stress optimization in the derivation of new accurate 8-node hexahedral elements for threedimensional elasticity. Equivalence of the proposed hybrid method to an enhanced strains method is established, which makes it easy to extend the method to general nonlinear problems. Numerical tests show that the resultant elements possess high accuracy at coarse meshes, are insensitive to mesh distortions and free from volume locking in the analysis of beams, plates and shells.