The phrase "military push-up" may conjure an image of some fantastically challenging form of an already demanding (but rewarding) exercise. How does a military push-up differ from a regular suburban American push-up? Not as much as you might think.
So assume the position and let's take a look at the various possibilities.
The Elbow Myth
In popular terms, a military push-up is commonly described as a push-up that emphasizes the triceps by keeping the elbows tucked to the sides. This would likely indicate a narrower spacing of hands than with a standard push-up, which usually assumes that the hands are spaced at roughly shoulder width apart.
Keeping your elbows tucked to your sides will indeed elicit more activation of the triceps, but to the best of anyone's knowledge, there has been no decree by the Joint Chiefs of Staff in regard to elbow placements and push-ups.
The Real Army Push-Up
The ability to do push-ups -- as well as sit-ups and pull-ups -- has long been considered an important measure of general fitness. And rightly so. Push-ups are a great indicator of not only upper body strength, especially the chest, shoulder and tricep muscles, but also general core strength and stability.
You may be surprised to learn that, other than the fact that army push-ups mean there's a drill sergeant ready to kick your butt if you don't maintain proper form, there's little or no difference between army push-ups and standard push-ups.