Humeral head translations (HHT) play a crucial role in the glenohumeral (GH) joint function. The available shoulder musculoskeletal models developed based on inverse dynamics however fall short of predicting the HHT. This study aims at developing a simulation framework that allows forward-dynamics simulation of a shoulder musculoskeletal model with a 6 degrees of freedom (DOF) GH joint. It provides a straightforward solution to the HHT prediction problem. We show that even within a forward-dynamics simulation addressing the HHT requires further information about the contact. To that end, a deformable articular contact is included in the framework defining the GH joint contact force in terms of the joint kinematics. An abduction motion in the scapula plane is simulated. The results are given in terms of HHT, GH joint contact force, contact areas, contact pressure, and cartilage strain. It predicts a superior-posterior translation of the humeral head followed by an inferior migration.