Strength Training for Muay Thai

I am not terribly experienced in muay thai, but I can tell you that the pressing movement with the biggest carry over to hitting/pushing against another person is the standing overhead press with a barbell (push presses are good too). Bench press is a good lift for upper strength and hypertrophy but the mechanics are far different than pushing a person; your feet aren’t your main base and you push completely horizontal to your torso. If you pushed an opponent away at that angle you would fall over backwards.