The contribution of this study is to propose a cohesive traction embedded constitutive law combined with shear-induced damage to represent the failure of metallic materials subjected to cyclic loading under various stress states. The proposed law accommodates a hyperelasticity-based plastic model with the use of the deformation gradient multiplicatively decomposed into separation-induced, elastic, and plastic parts. The plastic deformation gradient is further decomposed into energetic and dissipative parts to realize Bauschinger effect under cyclic loading. The energetic part of plastic deformation gradient contributes to an energy related to kinematic hardening and leads to a back stress. Moreover, to realize both shear-lip fracture and flat fracture under various stress states, both shear-induced damage and cohesive traction separation law are incorporated into the hyperelasticity-based plastic model. The shrinkage of yield surface that is caused by the rotation and elongation of voids in a shear band under low stress state is realized by the introduction of the shear-induced damage into the Tresca yield function. The evolution of shear-induced damage is determined by the damage loading function corresponding to the plastic energy release based on thermodynamics. On the other hand, the stress release process along with the material separation due to void nucleation, growth and coalescence under high stress state is represented by the combination between the separation-induced deformation gradient and the cohesive traction separation law. The capability of our proposed constitutive law is demonstrated by comparison with experimental results under various stress states including monotonic and cyclic loading