A reasonable and reliable numerical model for bracket sets is a critical issue in researching their hysteretic energy dissipating characterestics. Through the comparison and analysis of experimental results of 27 Song style bracket sets which were classified with four typical types, the characteristics of hysteretic curves and the associated key influencing factors for different types of bracket sets were identified. Based on these, a simplified hysteretic model, which can reflect the hysteretic characteristics of different types of bracket sets, was proposed. Furthermore, the determining method for the critical parameters of hysteretic rule was recommended. The results indicate that the Zhutou Puzuo and Bujian Puzuo types exhibit similar hysteretic characteristics. With the decrease of number of Tiao, the hysteretic curve becomes increasingly full. The hysteretic curve of the Chazhuzaotou Puzuo type exhibits significant pinching phenomena, which is more significant when the load is applied in the Huagong direction rather than the Nidaogong direction. The hysteretic curve of the Zhuanjiao puzuo type is the fullest. Comparison between simulated and experimental results indicates that the simplified hysteretic model and the corresponding determining method for critical parameters can accurately reflect the abovementioned characteristics of hysteretic curves and predict the total plastic energy of different types of bucket sets, thus validating the rationality and reliability of the simplified hysteretic model.