This part of study is devoted to the numerical simulation of axisymmetric notched specimens in order to study the phenomenon of nucleation by Gurson–Tvergaard–Needleman model (GTN). The numerical simulations were performed to describe the damage of the materials using GTN model, which involves the stress triaxiality. The specimens chosen are somewhat axisymmetric notched (AN): hence, this choice was motivated by the symmetry of these specimens, and also by the existence of notches that make them interesting in the case of fracture mechanics.