You can do a military press from a sitting or standing position, with barbells or dumbbells for resistance. Your triceps brachii, the pushing muscle at the back of your arm, primarily acts to straighten your arm at the elbow. Exercises similar to the military press -- such as the shoulder press and the Arnold press -- also work the triceps, as do triceps extensions, dumbbell kickbacks and triceps pushdowns.
Grasp the barbell or dumbbells with an overhand grip, hands slightly wider than shoulder-width apart, and position the weight in front of your neck. Press the bar or dumbbells straight overhead, then return to the starting position. Knowing which muscles you're working with this exercise will help you monitor and maintain proper form as you lift.
The anterior and medial deltoid fibers do most of the lifting in this exercise, bringing your humerus up as the triceps straightens your elbow. The deltoids, your primary shoulder muscle, are divided into three parts. Taken together, they resemble a three-clove bulb of garlic. The anterior deltoid lies across the front of your shoulder where your upper arm joins your torso. The lateral or medial deltoid crosses straight over the top of this joint, and the posterior deltoid lies behind it.
Although the military press might not seem like a core exercise, you must squeeze your abs tight in order to do it properly. If you don't squeeze your abs, your lower back might arch as you raise the weight overhead. Sitting down to do this exercise gives you immediate feedback on your body position; if you pay attention, you'll be able to feel your lower back pulling away from the bench if your form falters.
Although your triceps and deltoids are responsible for the primary movement, and your abs stabilize your spine as you lift, any exercise involving your shoulders will activate a number of other muscles. For the shoulder press, your trapezius, levator scapulae, serratus anterior and rotator cuff all work together to control your shoulder blades and stabilize your shoulder joint. The involvement of all these stabilizing muscles is one of the reasons free weight exercises are so effective; they force you to activate extra muscle fibers.