Rotator cuff tears are a common problem in patients over the age of 50 yr. Tear propagation is a potential contributing factor to the failure of physical therapy for treating rotator cuff tears, thus requiring surgical intervention. However, the evolution of tears within the rotator cuff is not well understood yet. The objective of this study is to establish a computational model to quantify initiation of tear propagation in the supraspinatus tendon and examine the effect of tear size and location. A 3D finite element (FE) model of the supraspinatus tendon was constructed from images of a healthy cadaveric tendon. A tear of varying length was placed at six different locations within the tendon. A fiber-reinforced Mooney–Rivlin material model with spatial variation in material properties along the anterior–posterior (AP) axis was utilized to obtain the stress state of the computational model under uniaxial stretch. Material parameters were calibrated by comparing computational and experimental stress–strain response and used to validate the computational model. The stress state of the computational model was contrasted against the spatially varying material strength to predict the critical applied stretch at which a tear starts propagating further. It was found that maximum principal stress (as well as the strain) was localized at the tips of the tear. The computed critical stretch was significantly lower for the posterior tip of the tear than for the anterior tip suggesting a propensity to propagate posteriorly. Onset of tear propagation was strongly correlated with local material strength and stiffness in the vicinity of the tear tip. Further, presence of a stress-shielded zone along the edges of the tear was observed. This study illustrates the complex interplay between geometry and material properties of tendon up to the initiation of tear propagation. Future work will examine the evolution of tears during the propagation process as well as under more complex loading scenarios.