Based on fluid-solid interaction mechanics theory, a coupled mathematical model for describing the slope stability of landfill under the condition of rainfall was developed. The model is used to evaluate the safety of the slope. The model simulates the effect of the slope gradient ratio and the slope angle on the slope stability under the different conditions of rainfall in the return periods. Results show that slope safety factor in the different rainfall conditions decreases with the increase in rainfall of time. When the slope gradient ratio is 1:2.5 and 1:3.0, slope safety factor decreased...