Abstract: On the dynamic equations of the softening nonlinear structural system, the convergence and stability of an explicit difference method presented by authors for solving the dynamic equations are analysedin this paper, and the stability conditions are given when the structural system is under the nonlinear positive stiffness state and the negative post-yield stiffness state. The results of the stability analysis show that as long as the stability condition is satisfied when the structuralsystem is under the visco-elastic state at the beginning of the structural response, the stability will be ensured in the whole process of integrating the response of the softening nonlinear structural system.