Abstract: Based on the elasto-plastic mechanics and continuumdamage theory, a yield criterion that relates to the spherical tensor ofstress is proposed to describe the mixed hardening of damaged orthotropicmaterials, and the dimensionless form of which is isomorphic with the Misescriterion of isotropic materials. Furthermore, the incrementalelasto-plastic damage constitutive equations are established. As an exampleof its application, the elasto-plastic buckling problem of the orthotropicrectangular thin plates with local damage are investigated by using theGalerkin method and iteration method, and the effects of geometricparameters and local damage on the critical buckling stress are discussed.