Train your upper back to do what?
I am talking about the bench press from a powerlifter's point of view. At times bodybuilders may bench press differently to target the pecs more, and even deliberately avoid leg drive as well (such as "feet up on bench" gahyness) to isolate the pecs even more. They will often bench with elbows flared out to weaken the back's contribution even more. Why? Different reasons for benching. One wants growth 'n size, the other (powerlifter) wants power and speed.
But, as I was saying, train your back cos all the drive comes from your back and lats when you are touching the bar to your chest. Then, add leg drive to turn your entire body into a taunt spring and your back comes into play even more so. A strong upper back, traps and lats will make for a big bench press. Often I have sore rear debts after a big bench session.
When benching "powerlifter style", you retract your shoulder blades down and back as hard as you can, flex or engage your lats (usually by trying to bend the bar or pull the bar apart, give it a try) and tuck your elbows in (not flaring them out). Add in powerful leg drive to keep your back tight and arched, and to force your upper back into the bench even more and you are a huge human bench press spring. If you do it right, you should not be flopping about on the bench. If someone was to push your knee inwards they should feel solid resistance.
When the bar is lowered to the chest, its the back that takes all the strain and it's the back and lats that get that most important explosive movement off the chest.
If you only want to train your chest, try dumbbells instead. They allow the hands to move inwards at the end of the rep, making the pecs more involved in the movement. A barbell, once you are over half way, stops the pecs from working and all the lock out movement comes from the triceps.
I think it was Dave Tate who said that if you set up tight and strong and correctly for a bench press, you should feel very uncomfortable.
So, to get a stronger bench, train your upper back and lats and learn to get that full body tightness, from toes to fingertips. It takes lots of practice to bring it all together.