In this work, we propose a method for monitoring and managing rotator-cuff (RC) tendon strains in human-robot collaborative physical therapy for shoulder rehabilitation. We integrate a high-resolution biomechanical model with a collaborative industrial robot arm and an impedance controller to provide feedback to a human subject, therapist or both, which prevents the subject from entering unsafe poses during rehabilitation. The biomechanical model estimates RC tendon strain as a function of human shoulder configuration, muscle activation and applied external forces. Subject- and injury-specific data are model estimates of strain that compose strain maps, which capture the relationship between the RC strains and movement of the shoulder degrees of freedom (DoF). High-strain regions of the strain map are identified as unsafe zones by clustering and ellipse fitting to smoothly demarcate these zones. These unsafe areas, which reflect increased risks of (re-)injury, are used to define parameters of an impedance controller and reference pose for real-time biomechanical safety control. Using strain maps we demonstrate both safe patient-led movements and teleoperated movements that prevent the subject from entering unsafe zones. In the teleoperated case, the physical therapist leads the patient remotely using a haptic device. The proposed method has the potential to improve the safety, range of motion, and volume of activity that a patient receives through robot-mediated physical therapy. We validated our approach using three experiments that demonstrate shoulder joint torques of less than 1 Nm during free motion with larger torques occurring only when the subject was asked to actively push into the unsafe boundary or, in the case of teleoperation, to resist the physical therapist.@en