Abstract: The sub-region mixed finite element is developed based on the sub-region mixed energy principle. It is a high-precision element, which is used to solve fracture problem and problems with notches and holes. In this paper, the stiffness matrix of the stress element in the sub-region mixed finite element method has been constructed. Spurious zero energy modes are present in the stress element, but it is proved that non spurious zero energy mode is present in the global analysis of the whole structure. The error estimate is systematically discussed under the condition of different number of stress terms or different element size.