Owing to the flammable, explosive, and toxic characteristics of hazardous chemicals, chemical accidents always result in significant losses. Analysis of the parameters of process safety is an effective way to prevent hazardous chemical accidents and reduce losses. To promote the application of systemic accident models in practice, in this study, we clarify the theoretical elements of such models based on the development of system thinking and system science. Then, we discuss the characteristics of a new systemic model called 24Model and its systems thinking. We explore the differences in the practical application of different systemic models (System-Theoretic Accident Model and Processes (STAMP), Functional Resonance Accident Model (FRAM), and 24Model by analyzing a major hazardous chemical explosion accident that occurred in Tianjiayi Chemical Co., Ltd. in China. The results show that the elements of the systemic accident model are the system structure, component relationship, and dynamic behaviors. 24Model is proven to be a new systemic accident model developed by utilizing sequential models. The comparative results of the three analysis methods show that FRAM is suitable for accident prediction rather than accident analysis. STAMP and 24Model perform better in terms of the usability and reliability of accident analysis. Although STAMP fails to elaborately indicate the internal organizational causes of the accident, it is suitable for a small number of accidents in socio-technical systems. 24Model is a structured method for accident analysis and safety management frame of organization. With the classified accident causes and fewer training resources, it is more suitable for a number of accidents statistics and analysis. Finally, a universal frame to prevent hazardous chemical accidents is provided for companies and regulators.