For this exercise, you'll need a trap bar, football bar, or Dead-Squat™ Bar. This is a great pressing alternative for people whose shoulders don't tolerate the bench press. And if you tweak the technique and turn it into more of a "squeeze" press, it can also be one hell of a chest blaster.
Neutral-Grip "Squeeze" Floor Press
It's going to look like a regular floor press with a few key differences. The devil is in the details. With the "squeeze" version, you want to set up with your lower back flat on the floor and try to purposely sink your chest down rather than puff it up.
After you un-rack the bar, bend your elbows slightly and flare them out. Then on the descent, rather than think about breaking the bar apart, think about squeezing your arms together, like you're giving someone a hug.
You won't be able to bring your arms together unless you possess superhero strength to bend metal, but the act of trying creates massive tension in the pecs. Keep that slight bend in your elbows and don't come all the way up at the top to keep constant tension on the pecs.
If you're using a Swiss bar or a football bar, use the handles that allow for a slightly wider than shoulder-width grip. If you're doing it right, you'll get a big pump with just the bar.