Abstract: The BFGS update method of second kind for two-level consistent secant operators is incorporated into the double scalar damage plasticity model. In order to make a good trade-off between computational efficiency and robustness, the quasi-Newton method is adopted to update the stiffness matrix and solve the equilibrium equation at structural level, and the BFGS update method of second kind is adopted to update the stiffness matrix for nonlinear material model. The one dimensional and two dimensional constitutive relationships of concrete are established based on the first and second kind of BFGS update method, and the two-level solution strategy is adopted to analyze the hysteretic behavior of reinforced concrete column and shear wall. The results reveal that both update methods are applicable to the beam element analysis, whereas the results of layered shell element analysis indicate that the BFGS update method of second kind has better numerical stability than that of first kind.