When the bucket foundation moves laterally or rotates, its sidewall may be separated from the soil to form a gap. The failure mechanism of the soil changes from "double-sided" to "single-sided", which reduces the bearing capacity. The three-dimensional finite element model was established to simulate the reaction between bucket foundation and cohesive soil. Two different types of contact types were set up, allowing separation or not allowing separation. 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 bearing capacity of the bucket foundation under different conditions was studied, and the capacity formulas of uniaxial and combined loading have been proposed. The results show that the separation of the bucket foundation from the soil reduces the uniaxial and combined bearing capacity, and the reduction is more significant with the increase of soil strength, while the aspect ratio has little effect on the reduction of bearing capacity. For uniaxial bearing capacity, it is recommended to quantify the impact of separation through the reduction factor. For combined bearing capacity, the normalized envelope surface expression that is suitable for both separation and not separation situations has been proposed.