The Tricep Muscle is the “three headed” (tri-cep) muscle on the back of the upper arm, opposite the bicep. I do not see much TRICEP TENDINOSIS. When I do, it’s usually in a weightlifter that has gone a bit overboard. I have never once seen the problem develop at the top of the muscle (near the shoulder). If it is going to occur, it will happen just above the back of the elbow.