New 4-node special hybrid stress membrane elements with drilling degrees of freedom have been developed based on an extended minimum complementary energy principle. These elements are used jointly with conventional displacement elements for the analysis of stress concentrations around different holes and notches. The assumed stress field in the elements satisfies the equilibrium equations, the traction-free boundary conditions and the compatibility equations. Detailed numerical studies show the new special elements can provide accurate stress concentration factors and the distributions of circumferential stress along the rims of the holes when only very coarse meshes are used near holes and notches.