Rehabilitation robots help the treatment of diseases by performing cyclic exercises for a long period of time. These exercises must perform movements of the patient’s limbs; thus, the robots are required to be flexible and safe. Among rehabilitation robots, cable robots are widely used due to their unique properties, such as being lightweight and the possibility of being equipped with magnetic hooks to improve both safety and ease of use. However, the elasticity and flexibility of cables result in vibrations of the payload and hooks. In this paper, the forced vibrations due to rehabilitation exercises are studied. Since the previous studies of the authors showed a weak coupling between longitudinal and transverse vibrations, a two-cable planar model for the study of transverse vibrations is developed. The model makes it possible to study the forced transverse vibrations due to both cable motion and robot motion. Stiffness and damping of the patient’s arm are considered. Results show that the cable system exhibits a simple linear behavior when excited by robot motion and a non-linear behavior when excited by cable motion.