Two tendons that attach the biceps muscle to the bones in the shoulder, the long head tendon that attaches the muscle to the top of the shoulder’s socket (glenoid) and the short head that attaches it to the shoulder blade. Tears are more likely to occur in the long head of the biceps tendon. Tears of the short head of the biceps are very rare. But even in case of a complete tear of the long head, the short head of the biceps may allow you to continue using your biceps muscle.