Tracking patient progress through a course of robotic tele-rehabilitation requires constant position data logging and comparison, alongside periodic testing with no powered assistance. The test data must be compared with previous test attempts and an ideal baseline, for which a good understanding of the dynamics of the robot is required. The traditional dynamic modelling techniques for serial chain robotics, which involve forming and solving equations of motion, do not adequately describe the multi-domain phenomena that affect the movement of the rehabilitation robot. In this study, a multi-domain dynamic model for an upper limb rehabilitation robot is described. The model, built using a combination of MATLAB, SimScape, and SimScape Multibody, comprises the mechanical electro-mechanical and control domains. The performance of the model was validated against the performance of the robot when unloaded and when loaded with a human arm proxy. It is shown that this combination of software is appropriate for building a dynamic model of the robot and provides advantages over the traditional modelling approach. It is demonstrated that the responses of the model match the responses of the robot with acceptable accuracy, though the inability to model backlash was a limitation.