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Catastrophe theory can describe a continuous process that is undergoing abrupt changes. A dynamic process can be considered a cusp catastrophe if it has the following five qualities: bimodality, sudden transitions, hysteresis, inaccessibility, and divergence. In this paper, the cusp catastrophe model is applied to describe the dynamic changing process of railway system safety. This dynamic process is also proved to have the five qualities of a cusp catastrophe. With the use of the cusp catastrophe model, a framework for the system risk of railway systems is constructed, and some ideas on the risk field of railway system safety are presented. On the basis of the framework and ideas, the dynamic changes in the system risk in a railway accident evolution process can be described in a novel approach. The concept of system risk in railway system safety is also discussed in three aspects. We hope that the theoretical …