This paper presents a systematic method for the dynamic analysis of flexible mechanical systems containing closed kinematic loops. Kinematics between pairs of contiguous flexible bodies is described with the joint coordinates and the deformation modal coordinates. The cut-joint constraint equations associated with the closed kinematic loops are derived, simply using the geometric conditions. The equations of motions are initially written in terms of the joint and modal coordinates using the velocity transformation technique. Lagrange multipliers associated with the cut-joint constraints for closed-loop systems are then eliminated systematically using the generalized coordinate partitioning method, resulting to a minimal set of equations of motion.