Pushing anything overhead is an awesome way to build thick shoulders and triceps, but it's tough to achieve that effect with bodyweight moves. Enter the pike pushup.
Pike pushups mimic overhead lifting by getting you upside-down. Get into a pushup position and raise your hips until your upper body is vertical from your hands to your hips. It's probably easier to achieve this position if you set your feet on a box or bench. Doing a pike pushup with your feet in a suspension trainer, as shown here, will challenge your balance but still let you scale down the load on your shoulders.
Keep your elbows in as you descend, drive yourself back up, and keep your hips up the entire time. Make sure your fingers are pointing in front of you, rather than out to the sides.