When the bucket foundation moves laterally or rotates, its sidewall may separate from the soil and cause a gap. The capacities decrease because the failure mechanism of soil changes from “bilateral” to “unilateral”. The three-dimensional finite element model was established to simulate the reaction between bucket foundation and clay. Two different types of interaction, allow to separate or not allow to separate, were set. The soil strength and aspect ratio of the bucket foundation were varied to determine the conditions when separation occurs. The effect of the separation on the capacities under different conditions was studied, and the capacity formulas were proposed. The results show that: separation reduces the uniaxial and combined capacities, and the reduction is more significant with the increase of soil strength, while the aspect ratio has little effect on the reduction of bearing capacities. For uniaxial capacities, the influence of separation was suggested to be quantified by the reduction coefficients. For combined capacity, the normalized envelope, which suits both separation and not separation situations, was proposed.