Unlike a single universal joint, in which the output shaft rotates with a fluctuating speed depending on the misalignment angle, a double universal joint is used to connect two offset shafts. If a double universal joint is correctly arranged, with equal joint angles in perfect alignment, the output shaft rotates in a synchronous motion with uniform speed. However, in practice, the intermediate shaft of a double universal joint system suffers from bending moments induced by joint friction and velocity fluctuation induced by the joint angles. These factors distort the linear relationship between the input and output shafts. In this paper, the effects of joint angles and joint friction on the steady-state responses of a double universal joint system are examined. The mass matrix, damping matrix, stiffness matrix, and nonconservative force of a universal joint are derived analytically for finite element modeling. The formulation introduced generates an elementary matrix suitable for the analysis of complex rotor-bearing systems that include double universal joints.