Abstract: Due to the implicit nature and the large quantity of stress constraints, topology optimization for plate and shell structures with stress constraints is difficult to construct. In order to overcome these issues, the element weight penalty function and the material allowable stress penalty function are introduced to the solid isotropic material penalization (SIMP) method by analogizing the filter functions in the independent continuous and mapping (ICM) method. The concept of penalty functions in the SIMP method is extended. Subsequently, the stress constraint globalization strategy in the ICM method is transferred into the extended SIMP method. The approximated explicit functions of the structural distortion energy constraints are formulated to replace the stress constraints. Finally, topology optimization for plate and shell structures in various loading scenarios are constructed and solved by the dual sequential quadratic programming method. The optimization programming is implemented on the platform of Abaqus software package based on the Python script language. Good results are obtained by implementing the proposed approach in several examples, which show the feasibility and efficiency of the proposed approach.