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The main aim of the work was to estimate effect of the constraint on the predicted crackpath and show the cases where the failure of the component could be described moreprecisely by constraint-based description. A special specimen geometry with a highlevel of constraint was used. Numerical predictions of the crack path in a modified CTspecimen are compared with experimental results. The numerical model was built usingcommercial software ANSYS and a special procedure for the crack propagation wasdeveloped. The numerical prediction of the crack path based on a modified MaximumTangential Stress (MTS) criterion (the criterion uses a two-parameter description of thestress field around the crack tip) is generally in agreement with the experimental data.The classical MTS criterion was found much more sensitive on the crack increment. Itcan therefore be concluded, that the modified criterion in the framework of two-parameter linear elastic fracture mechanics estimated the crack path more preciselyonly in the case of a high level of constraint.