<p>Non-extreme flood disasters caused by urban fluvial flooding can disrupt and impact the operation of urban road traffic systems. This is particularly evident in the influence on the path selection behavior of network users and the resulting changes in the equilibrium state of the road network. Consequently, the network cannot maintain its original performance, leading to disturbances and interruptions. Therefore, this study proposes a novel stochastic traffic assignment model to simulate and analyze such scenarios. The model proposed in this study introduces a path cost expression that incorporates two stochastic terms, effectively capturing the perceived objective costs for different types of users under non-extreme flooding: flood risk and travel time, as well as the subjective cost factors of the users. Additionally, this study introduces a new criterion to classify paths into acceptable and unacceptable categories. Users will abandon unacceptable paths deemed too dangerous and will choose paths only from their set of acceptable paths until the road network reaches an equilibrium state. The corresponding set of acceptable paths will dynamically change based on the risk sensitivity of different types of users and the prevailing flood conditions. The model developed in this study can effectively analyze the impact of non-extreme floods on the path selection behavior of users with different risk sensitivities and simulates the evolution of the road network’s equilibrium state as users instinctively avoid risks. This research provides valuable insights for stakeholders in the operation, management, maintenance, and restoration of road networks under non-extreme flood conditions.</p>