The Richards’ equation describes the flow phenomenon in unsaturated porous media and is essential to hydrology and environmental science. This study evaluated the numerical stability of two different forms of the Richards’ equation. Sensitivity analyses were performed to investigate the control parameters of the equation. The results show that the h-form Richards’ equation has better applicability for calculating variable saturation flows than the θ-form Richards’ equation. For the h-form Richards’ equation, the hydraulic conductivity of the soil in the low-suction range and the specific moisture capacity in the high-suction range primarily influenced the solution. In addition, sensitivity analyses indicated that the saturated hydraulic conductivity, initial condition, and air-entry pressure have a higher sensitivity to the simulation results than the saturated water content, rainfall intensity, and decline rate of hydraulic conductivity. Moreover, their correctness needs to be guaranteed first in numerical simulations. The research findings can provide a helpful reference for improving the reliability of numerical simulations of unsaturated flows.