The definition of a traction-separation relationship is a fundamental issue in cohesive zone models because it describes the nonlinear fracture process.Cohesive interactions are generally a function of displacement jump (or separation).If the displacement jump is greater than a characteristic length (n), complete failure occurs.In this study, the softening condition behavior of a cohesive interface between two identical materials was assessed for different stiffness values of solid and cohesive.The cohesive interface was modeled with a traction-separation linear relationship and for the solids continuum elastic constitutive models were used.The softening condition was obtained by analytical and finite element method.The whole system behavior was modeled using ABAQUS 6.14 to obtain stress-displacement relationship.The analytical solution and computational results were compared.The computational results matched the analytical solutions and the simulations allowed to obtain a response in the cases where the analytical solution has singularities "backslash effect".