Separation work rate as a function of the crack extension in a thin curved compact tension (CCT) specimen of Zr-2.5Nb pressure tube material is investigated by three-dimensional finite element analyses with the finite step nodal release method. The straight crack front for the crack extension is assumed. The crack extension is simulated by releasing the nodal points ahead of the initial straight fatigue crack front in the CCT specimen. The crack extension follows the available experimental crack extension-displacement data. The computational results show that the plastic zone size and shape change along the crack front as the crack extension increases. The computational results also show that the separation work rate is a function of the crack extension and is similar to the experimental J-R curve. The computational results suggest that in a two-dimensional finite element analysis of the crack extension in the thin CCT specimen with the cohesive energy approach, the cohesive energy can vary to account for the change of the constraint conditions along the crack front as the plastic zone size increases with the crack extension.