It is understood that accurate modelling of the mechanical behaviour of tendon tissues is vital due to the tendon’s essential role in the facilitation of joint mobility in biological mechanisms. The supraspinatus tendon helps to maintain dynamic stability at the glenohumeral joint in conjunction with other rotator-cuff tendons, namely infraspinatus, subscapularis and teres minor. These tendons are thought to support the action of the more powerful forces that are innovated at that joint by the deltoid, pectoralis major, biceps and triceps muscles. The supraspinatus tendon is often prone to injury especially in careers or sporting activities that involve frequent arm abduction. It is therefore important to understand the mechanical behaviour of this tendon in order to devise better rehabilitation therapies in case of injury. This paper evaluates the relative modelling capabilities of three hyperelastic models, namely the Yeoh, Humphrey and Veronda-Westmann material models on the tensile behaviour of three tendon specimens. We compare their fitting accuracies, convergence rates during optimisation, and the different forms of sensitivities to data-related features and initial parameter estimates. The results show that the Yeoh model outperforms the other two hyperelastic models and therefore makes it relatively better choice for further investigation of the mechanical behaviour of tendons.