This study presents that continuum-damage-model-like constitutive laws combined with Tresca-type and Mises-type yield functions are compared to realize shear band that develops into shear-lip fracture under low or negative stress triaxiality state. The CDM-like constitutive laws are developed by a hyper-elasticity based plastic model with the use of the deformation gradient multiplicatively decomposed into separation-induced, elastic and plastic parts. The elastic–plastic deformations along with the isotropic hardening are represented by a Hencky-type model combined with the Tresca-type or Mises-type yield functions, respectively. In addition, the strain softening at the strain localization are realized by the introduction of shear-indued damage variable into both yield functions as the shrinkage of the yield surfaces. The evolution of the shear-induced damage variable is represented by the damage-loading function corresponding to the plastic energy release based on thermodynamics. On the other hand, the stress release process caused by flat fracture is realized by cohesive traction separation law and the assumption of the local equilibrium state between the principal stress and cohesive traction. By comparing with experimental results, the difference of the numerical results of the CDM-like constitutive laws with Tresca-type and Mises-type yield functions are demonstrated throughout various types of specimens under different stress states.