In this study, a cable-driven exoskeleton device is developed for stroke patients to enable them to perform passive range of motion exercises and teleoperation rehabilitation of their impaired hands. Each exoskeleton finger is controlled by an actuator via two cables. The motions between the metacarpophalangeal and distal/proximal interphalangeal joints are decoupled, through which the movement pattern is analogous to that observed in the human hand. A dynamic model based on the Lagrange method is derived to estimate how cable tension varies with the angular position of the finger joints. Two discernable phases are observed, each of which reflects the motion of the metacarpophalangeal and distal/proximal interphalangeal joints. The tension profiles of exoskeleton fingers predicted by the Lagrange model are verified through a mechatronic integrated platform. The model can precisely estimate the tensions at different movement velocities, and it shows that the characteristics of two independent phases remain the same even for a variety of movement velocities. The feasibility for measuring resistance when manipulating a patient’s finger is demonstrated in human experiments. Specifically, the net force required to move a subject’s finger joints can be accounted for by the Lagrange model.