The barbell bench press is a classic strength exercise, and classically troublesome for people who have shoulder problems. When performed correctly, the bench press is an effective exercise to improve chest, shoulder, and triceps strength. When performed incorrectly, certain structures in the shoulder joint can become irritated and produce painful consequences.
Proper bench press technique relies more on getting the shoulder joint in a correct set position before and during the pressing movement rather than on whether or not the bar should come down to touch the chest. That is, if you can put your shoulder blades in a stable packed position where they are set slightly toward each other and downward throughout the bench press exercise, then your shoulder joint (and the structures surrounding it) will fare better because they will have the appropriate space in which to move. Therefore, if the shoulder blades are in the correct position throughout the movement, touching the bar to the chest should not be a problem. The problem most people run into with bench pressing and shoulder pain is that they have rotator cuff dysfunction in which the small muscles of the rotator cuff are not doing an adequate job of holding the head of the humerus in its proper path during the movement. This allows the head of the humerus to migrate into areas never intended, and consequently the tendons and nerve structures associated with the rotator cuff can become inflamed and impinged. Therefore, the recommendation for people with shoulder instability due to rotator cuff dysfunction is to keep the elbows flexed at 90 degrees and not allow the bar to touch the chest.
Another issue with bench press and shoulder pain is the level of arm abduction, which can be visualized by where the elbows are during the movement. If the elbows are in the lateral plane as the shoulders, impingement and pain are likely to occur. If the elbows remain below the shoulder (more toward the ribcage), the head of the humerus is less like to smash the soft tissues of the shoulder joint. But again, elbow/arm placement can also be related to rotator cuff dysfunction, so these two issues are tied together.
If pain is present during the bench press exercise and it is not relieved by lowering the load and setting the shoulder blades in the appropriate position, the exerciser should have the affected shoulder evaluated by a physician before continuing upper-extremity exercise. This way, the cause of the pain (e.g., rotator cuff dysfunction) can be addressed and cleared prior to working on upper-extremity strength with exercises such as the bench press.