Musculoskeletal models enable movement scientists to examine muscle function by computing the mechanical work done by muscles during motor tasks. To estimate muscle work accurately requires a model that is physiologically plausible. Previous models of the human shoulder have coupled scapula movement to humeral movement. While coupled movement produces a stereotypical scapulohumeral rhythm, it cannot model shrugging or independent movement of the scapula and humerus. The artificial coupling of humeral elevation to scapular rotation permits muscles that cross the glenohumeral joint, such as the rotator-cuff muscles and deltoids, to do implausible work to elevate and rotate the scapula. In reality, the motion of the scapula is controlled by thoracoscapular muscles, yet the roles of these muscles in shoulder function remains unclear. To elucidate the roles of the thoracoscapular muscles, we developed a shoulder model with an accurate scapulothoracic joint and includes scapular muscles to drive its motion. We used the model to compute the work done by the thoracoscapular muscles during shrugging and arm elevation. We found that the bulk of the work done in upper-extremity tasks is performed by the largest muscles of the shoulder: Trapezius, deltoids, pectoralis major, and serratus-anterior. Trapezius and serratus anterior prove to be important synergists in performing upward-rotation of the scapula. We show that the large thoracoscapular muscles do more work than glenohumeral muscles during arm-elevation tasks. The model, experimental data and simulation results are freely available on SimTK.org to enable anyone to explore our results and to perform further studies in OpenSim 4.0.