The synthesis of shoulder kinematics, either for simulation in a model or imitation in a robot, is a challenging task because of the contact between shoulder blade and ribcage. As the shoulder moves, the shoulder blade glides over the ribcage. In kinematic mod- els used to predict musculoskeletal kinetics, the contact is included using equality con- straints, creating interdependencies between the kinematic coordinates. Such interdepen- dencies make motion planning complex. Robotic mechanisms often imitate the shoul- der’s end-effector kinematics but not the gliding shoulder blade architecture. It is only recently that a gliding shoulder blade architecture has been mechanically achieved. The goal of this paper is to propose a novel kinematic parallel model of the shoulder that includes the contact without using constraints. Mechanically, the gliding architecture is replaced with a parallel architecture. A shoulder model with constraints is used to build the parallel model. It is shown that replacing the contact constraints with kine- matically equivalent kinematic chains, leads to a 2–3 parallel platform model of the shoulder. The scaffold model and parallel model parameterisations of the shoulder’s kinematics are analysed in terms of the forward kinematic map. The coordinate spaces of the kinematic maps are analysed, resulting in three minimal parameterisations. Each minimal parameterisation uses a set of coordinates equal to the number of degrees of freedom. The minimal coordinates are independent and considerably simplify motion planning.