When suction caissons are used as foundation of the manifold or pipe terminal in deep waters, they are subjected to a torsion except for the vertical force, horizontal force and moment applied. The torsion may reduce the vertical, horizontal and moment bearing capacities of caisson foundation. In this study, theoretical analyses and finite element simulations are conducted to study the interaction between normally consolidated clay and the typical caisson (with a length-to-diameter ratio between 1 and 2) subjected to combined loadings. The strength reduction of the soil around the caisson skirt induced by installation are considered in the theoretical and numerical analyses. For caissons under undrained conditions, the uniaxial torsion capacity and the influences of the torsion on the other capacities are obtained. The results show that when it is less than 20% of the torsional capacity, the torsion applied has slight effect on the vertical, horizontal or moment capacities. When torsion applied reaches 20%~80% of the torsional capacity, the other three capacity components can be reduced by as much as 20%. The torsion influence factors against three capacities are proposed for routine designs.