Abstract Painful cuff tear arthropathy (CTA) affects the independence of the elderly. Surgical treatment often consists of joint replacement, the functional outcome of which remains variable. Knowledge of the biomechanical properties of the different prosthetic designs can guide the orthopaedic surgeon in the choice of implant to predict its clinical result. A 3-D computer model of the glenohumeral joint is used to analyse the moment of the deltoid muscle in the scapular plane. A geometrical 3-D ball-and-socket model of the shoulder joint was used to calculate (1) the angle–force relationships, (2) the moment arm of the deltoid muscle and (3) the moment of the deltoid muscle components, for increasing degrees of arm elevation in the scapular plane. In this 3-D model, a clinical thoraco-scapular rhythm analysis was implemented, based on measurements in normal subjects, patients treated with an anatomical prosthesis and patients treated with an inversed delta III prosthesis ®. These data were compared for 10 different prosthetic treatment options. Results. Muscle angle–force curves show a favourable slope in non-anatomical prosthetic designs, where the centre of rotation of the glenohumeral joint is medialized, the deltoid muscle is elongated and the humeral shaft is lateralized. On the contrary, anatomical prosthetic designs do not perform well in this computer analysis. Conclusions. From a biomechanical point of view, a shoulder prosthesis which medializes the centre of rotation, lengthens the deltoid muscle and increases the deltoid lever arm, results in a significantly more powerful abduction of the shoulder, despite complete loss of rotator cuff function. Relevance. This study explains why a successful functional outcome can be expected in CTA with a reversed prosthesis.