The out-of-plane stress of composite laminated plates and shells is of great significance to the initiation and expansion of interlaminar delamination. Firstly, the formulation of classical non-compatible displacement finite element is given out briefly. And then, based on the modified Hellinger-Reissner (H-R) principle, the relationship between out-of-plane stress variables and displacement variables is derived. The finite element linear system of out-of-plane stress provides convenience for the introduction of out-of-plane stress boundary conditions. At the same time, the uniqueness and continuity of the out-of-plane stress at the node can be obtained directly by the finite element linear system. Compared with the results of non-compatible displacement finite element method, the proposed method can improve the accuracy of numerical results obviously, and the computational efficiency and resource requirements are superior to the non-compatible symplectic element method and the non-compatible generalized mixed element method.