The mobility of the healthy shoulder depends on complex interactions between the muscles spanning its glenohumeral joint. These interactions ensure the stability of this joint. While previous studies emphasized the complexity of the glenohumeral stability, it is still not clear how the kinematics and muscles interact and adapt to ensure a healthy function of the glenohumeral joint. To understand the function of each muscle and degree of freedom of the glenohumeral joint in executing an above-the shoulder box handling task while ensuring stability, we adapted an index-based approach previously used to characterize the functions of the lower limb joints and muscles during locomotion. Forty participants lifted two loads (6 Vs. 12 kg) from hip to eye level. We computed the mechanical powers of the glenohumeral joint and its spanning muscles. We characterized the function of muscles and degrees of freedom using function indices. The function of the glenohumeral joint underlined its compliancy and design for a large range of motion, while the rotator cuff indices emphasized their stabilizing function. The overall muscle functions underlined the complexity of the glenohumeral stability that goes beyond the rotator cuff. Additionally, the load increase was compensated with changes in the functions that seem to favor joint stability. The implemented approach represents a synthetized tool that could quantify the glenohumeral joint and muscles behavior during tridimensional upper limb tasks, which might offer additional insight into motor control strategies and functional alterations related to pathologies or external parameters (e.g., load).