Abstract: The equation of damping moment due to the elastic deformation of bellows shell is derived by the minimum potential energy principle, and the relations between joint angle and damping moment are gained. The result is nearly the same as that of force balance method. Thusly, the method was proved valid by comparison. The influences of joint’s geometry parameters and elastic deformations of bellows shell on moment are analyzed. The results show that the adding arc size of bellows or reducing space between two bellows can make a damping moment for joint reduce, and the influence of the elastic deformation to joint damping moment is very small in a certain range.