One of my favorite exercises to build muscle mass and strength at the same time is the bench press. This compound exercise works the chest, shoulders, and triceps as its primary movers and can even tap into the entire body for stability.
One of the best resources for increasing your bench press is the Boost Your Bench press website found at http://www.boostyourbenchpress.com/. This site contains training programs and tips for increasing your bench press strength. Below, I will go over some of my favorite tips from this website so you can apply it to your own regimen to increase your bench press.
The first way to improve your bench press is to just make sure you bench press all the time. If you try to supplement your bench press with other chest and shoulder exercises but never get around to frequently bench pressing, do not be surprised when your bench press never increases. You almost always want to bench press first in your chest workouts because your muscles will be fresher that way and you will be able to handle more weight. Stick to other chest exercises later in the workout after you have put in your highest quality work on the bench.
Another important aspect of increasing your bench press strength is building muscle. To build muscle, you need to not only work out regularly, but you also need to eat enough calories and protein. Muscle just does not come out of thin air. It requires a lot of protein and water to build. However, not only that, but if you are not eating enough food, your body will not give you the protein to build muscle but instead will digest it and use it for energy. Make sure you eat a lot and eat a lot of protein while working out and all the time if you want to get stronger on the bench press.