Two different approaches that explicitly incorporate the stress triaxiality into cohesive zone models applicable to thin-walled structures are compared to identify the relative merits and limitation of these models. The number of model parameters involved, the ease of parameter determination and the predictive capabilities of the models over a wide range of thin-walled geometries are investigated. The first model, proposed recently by the authors, uses basic elastic-plastic constitutive equations combined with a model parameter depending on the average triaxiality in plane stress conditions. The second model incorporates stress-state through exponential dependence of cohesive strength on triaxiality, similar to plane strain studies earlier. The respective parameters for both models are identified and subsequently applied to several notched and precracked specimens. It is shown that in contrast to stress-state independent models, both constraint dependent models are able to predict well failure of a wide range of structures. While the model incorporating triaxiality dependent cohesive parameters has more parameters to be determined, it is not restricted to any specific stress condition and therefore can be extended to arbitrary three-dimensional stress-states. © 2010 Elsevier Ltd.