In the case of rainstorm, instability accidents in tailings ponds occur frequently, but there is no reliable calculation method for the stability calculation of tailings ponds. At the same time, there are problems of fuzzy hydrological boundaries and randomness of geotechnical parameters in the stability analysis of tailings ponds, which greatly weakens the credibility of the stability calculation. Therefore, this paper studies the stability of tailings ponds by using the principle of hydrogeology, the theory of elastic-plastic mechanics, the idea of limit equilibrium, and the probability analysis model. The boundary conditions of rainfall slope of tailings ponds are determined based on hydrogeological rainstorm analysis and trapezoidal generalization method. The potential sliding surface of tailings pond slope is solved by using the limit strain criterion. Through the random sampling method of Monte Carlo parameters to deal with the randomness of slope geotechnical parameters, the limit strain Monte Carlo reliability analysis method is established. Finally, through the calculation of practical cases, the stability results of tailings ponds under rainstorm are analyzed. The research results provide ideas for the quantitative analysis of tailings pond stability and have important significance for engineering guidelines.