Primate glenohumeral morphological features are frequently used to infer functional demands in living and extinct taxa. This mapping of form-to-function is confounded, however, when applied to fossils that display a mosaic of features with different functional associations. Here, we present a quantitative “six-degree-of-freedom” model and predict the glenohumeral range-of-motion (ROM) of nine living and fossil species from skeletal geometry, sampling hominoids and Old World monkeys. We simulated 82584 positions spanning all three rotational degrees of freedom and defined the ROM as positions where the humeral head and glenoid maintain congruence. We quantified mobility – a function of the size of the ROM – and a functional region – the abduction angle around which the joint has its most rotational freedom. Primates who engage in suspensory activity (ie. gibbon, orangutan, and chimpanzee) had greater mobility and higher functional regions compared to more terrestrial quadrupeds such as the gorilla and mandrill. The ROM of modern humans was intermediate. Interestingly, Australopithecus sediba, a fossil hominin suggested to have retained arboreal traits, exhibited ROM characteristics most similar to humans. Our model captures the complex interaction between features on articulating surfaces, allowing us to predict ROM that is not evident from comparisons of discrete morphological traits. For instance, the difference in ROM of the chimpanzee and gorilla is consistent with observed locomotor behavior, despite qualitative similarities in bone features. This framework enables a thorough functional interpretation of glenohumeral morphology and can be used to reconstruct the forelimb function of ancestral nodes in primate evolution.