Based on the principle of minimum action and taking time as the minimum action quantity, the functional of two-dimensional Richards equation was established. The variational solution of soil slope water infiltration under ponding was proposed. Brooks-Corey model was used to calculate the hydraulic slope of soil mass and the shape of the infiltration curve was discussed. Hydrus 2D software was used to analyze the water content distribution in the slope under the first type of boundary conditions. The results show that the variational solution of the 2-D infiltration has the same form as that of the 1-D horizontal infiltration and vertical infiltration. The infiltration path is convex shape. The infiltration capacity is linearly related to the depth of the wetting front, which is consistent with the results obtained by variational solution. Therefore, the depth of wet front and the distribution of water content obtained by the variational solution are feasible to analyze the macro-engineering problems such as slope stability.