Abstract: New 8-node special hybrid stress elements with drilling degrees of freedom have been developed based on the principle of minimum complementary energy. These elements are used jointly with conventional displacement elements for the analysis of stress concentrations around different holes and notches. The assumed stress fields in the elements satisfy the equilibrium equations, the traction-free boundary conditions and the compatibility equations. The examples of these special elements have been shown that these present special elements are far superior in predicting the stress concentration factors, the distributions of circumferential stresses and the normal stress when only very coarse meshes are used near holes and notches.