With the rapid development of urban rail transit, the problems of structural corrosion caused by stray current are becoming more and more serious. According to the electrical parameters and soil data of an urban rail transit, this paper calculates the stray current in CDEGS software with a four-layer conductor structure of “rail - discharge network - structural reinforcement - earth”. When considered the frequent occurrence of extreme rainfall events, the effect of uncertainties in parameters such as soil resistance and rail-to-ground transition resistance on the stray current are quantitatively evaluated based on Monte Carlo algorithm. The results show that the changes in soil moisture, soil resistance and rail-to-ground transition resistance triggered by extreme rainfall will increase the stray current of the rail significantly, and the stray current exceeding 0.5 A is about 18%. Hence, attentions are required to both the risk interval of the stray current and rail bottom potential for effective protection against stray current.