A new stress assumption for hybrid stress elements is presented. Generalized incompatible modes are proposed and incorporated into the constraint equations for assumed stresses. The physical meaning of the resulting constraint equations is discussed. The present stress assumption, which can consider the mesh distortion more rigorously, is based on the physical interpretation of the role of the generalized incompatible modes and substantiated with simple mesh distortion measures defined in this paper. The stress assumption is adapted to the previous four-node hybrid stress element, 5 beta-I and the eight-node hybrid stress brick element, 18 beta, which results in a new four-node plane element, M5 beta and an new eight-node brick element, M18 beta. Numerical results show that the refined elements are noticeable in low sensitivity to mesh distortion and in high-accuracy of stresses. (C) 1997 by John Wiley & Sons, Ltd.