Close-grip pushups, pushups on stability ball, power pushups, regular pushups, incline pushups, decline pushups, uneven pushups....take your pick! Pushups are one of the all-time best bodyweight exercises.
The pushup on medicine ball is a tough exercise that not everyone can do! Case in point: I was at the health club one day and a former marine was working out. I started to talk to her about the pushup on medicine ball and she tried the move (of course!). She was shocked to find out that she couldn't do one pushup on the medicine ball!
I'm guessing that she has progressed to the point that she can probably do a few of them now! In true marine-like fashion, she vowed to "conquer" the pushup on medicine ball!
How to do the movement: Put both hands on the ball at arms length. Keep your body straight and torso braced (as if taking a punch in the gut) throughout the movement. Keep your head in line with your torso at all times. Lower your body down to the ball and back to starting position. Repeat as required.
This type of pushup requires adequate core strength to do it properly. The pushup on medicine ball will build your upper body stabilizer muscles (chest, arms, shoulders, core, etc.) needed to increase your bench press or other upper body strength exercises.