IMO, the most common cause of shoulder pain, when bench pressing, is when the internal rotators to external rotator cuff strength is imbalanced (in favor of the internal rotators).
This imbalance is usually caused by the lack of rowing work that is done in relation to chest pressing. Most of the time, making sure there is a balance between horizontal pulling (rowing) and horizontal pressing (benching) is all that is needed to prevent the problem.
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What happens if there is already an imbalance? Charles Poliquin wrote an excellent article on this subject. He uses the close-grip bench press, in this article, because it was more specific for his subject's sport. What he did was test the subject's close-grip bench press and external rotation exercise. He found that your external rotation (8RM) should be 9% of your close-grip bench press (1RM). If you close-grip bench press 1RM is 300lbs, then your external rotation should be an 8RM of 27lbs, approximately.
With all the predominant horizontal pressing programs, out there, this can give you an indication if there is a balance between the internal rotators and external rotators of the shoulder. For those that are addicted to the bench press, strengthening the rotator cuff will increase your bench in the long run. You are only as strong as your weakest link.
Another interesting topic, in this article, was about the use of the behind-the-neck press.
A number of years ago, my training partner was a physical therapist and I would ask questions about contraindicated exercises. The PT said that as long as you do not feel pain, in the ROM, behind-the-neck presses are a fine addition. That surprised me because most PT's would not recommend them. Charles Poliquin says that the issues can range from "a tight subscapularis to a weak infraspinatus". Once these issues are addressed, the exercise can be added.
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My question is, do you think that internal rotator cuff exercises are even necessary to perform? Since most already have internal rotator dominated programs, wouldn't it be a better idea to just focus on external rotation strength? The reason I ask is because I will still see people doing internal rotation exercises in their rotator cuff program. I thought it would be an interesting topic to discuss.