Abstract: The outer wall steel pipes and even the steel reinforcement of steel pipe concrete columns are prone to local buckling during compression process under strong seismic loading, and the numerical simulation of the rod model cannot describe the real structural seismic response if the cyclic constitutive model does not take into account the change in the load carrying capacity of the outer wall steel pipe and the steel reinforcement after buckling (it cannot satisfy the demand on the accuracy of describing the real and complex response). In the numerical model of the outer wall steel pipe, its buckling behaviour is simulated at the plate level. In order to study the hysteresis characteristics of the steel (plate) specimens under complex cyclic paths after buckling, the paper takes 66 steel specimens of Q235 and Q420 as the research objects and designs various loading regimes to simulate the randomness of earthquakes. By analyzing the test results and comparing the simulation verifications of GA model and DM model, it is found that the existing models can only satisfy the case of simple tension or axial compression. In order to accurately describe the elastic-plastic buckling behaviour of steel under cyclic loading, this paper combines the GA model with the DM model and proposes a modified relationship model for the three stiffness of the buckling and re-stretching paths, which is verified through a comparison with experimental data that the model can reasonably predict the hysteresis-return eigenstructure relationship of steel after compression buckling with high accuracy.