Abstract： A cohesive zone model for model III crack in powerlaw hardening was studied under small scale yielding conditions. The cohesive tractionseparation displacement in the cohesive zone and the stressstrain fields were obtained. The results show that the stress distribution in a large portion of the plastic zone is significantly altered with the introduction of the cohesive zone, for a modest hardening material, if the peak cohesive traction is less than 2.5 times yield stress, which implies that the disparity in terms of the fracture prediction between the classical approach of elasticplastic fracture mechanics and the cohesive traction becomes infinitely large. When the peak cohesive traction becomes infinitely large, the stress distribution with and without the cohesive zone converges.