In this study, we propose a novel polymer rupture model that focuses on the transition from elastic to softening deformation under mechanical stimuli. Starting with the end-to-end vector approach and drawing from the Finitely Extensible Nonlinear Elastic (FENE) model, we develop a criterion for polymer breakage. This model improves upon previous approaches that lacked clear mechanical rupture criteria. The method involves addressing singularities in the FENE model by introducing the γ term in the second-order expansion of spring deformation, allowing for a transition from elastic to softening deformation. As the force diminishes, rupture eventually occurs. Furthermore, we derive a continuous version of the model to perform simulations, comparing it with other viscoelastic classic models of viscoelastic fluids.