The five major forearm muscles: brachioradialis, pronator teres, flexor carpi radialis, palmaris longus and flexor carpi ulnaris all get a major workout anytime someone takes to the mountain. Since the muscles in the fingers themselves are very tiny and hard to exercise, the strength it takes to hold you onto the face of a rock are found in the forearm. For this reason, many climbers strengthen their forearms by completing hand exercises. Squeezing a grip bar or small ball several times in the hand will ultimately improve hand, wrist and forearm strength, increasing your endurance and allowing you to stay hugged against the wall tightly.
The ability for a climber to hang by the arm or pull themselves up by the arm when a footing is too small comes mostly from the upper arms and shoulders. These muscles include the bicep in the front of the arm, the triceps behind the arm and the deltoid that wraps around the shoulder. To increase strength in these muscles, many climbers do repetitions of pull-ups. While pull-ups work well to increase strength in the arms, too many repetitions can result in injury. Consider reducing the number of repetitions anytime pain is felt.
Any seasoned climber knows that, while climbing most certainly does take arm strength, the real strength comes from the legs. Climbers do not use their arms to lift their bodies; the arms are used predominately to stay tight against the mountain. To move up a rock face a climber must use her quadriceps muscles, found in the front of the thighs. Strong quadriceps allows a climber to step up from any precarious angle. Strengthen the quadriceps by doing squats and always taking the stairs, two steps at a time, instead of an elevator.
The muscles in the calves, although used less to help a climber step up than the quadriceps, also play a crucial part in climbing. When a wall's face has small nooks and crevices, the calf muscles are what aid you to keep your toe against the wall when only the smallest bit will fit. When it comes time to move upward, it is the calf muscles that allow you to rise to your tip-toes to get a better reach. For the fastest way to increase calf strength, simply rise to the ball of your feet and lower back down several times while standing. It will not be long before you feel the burn. Alternate patterns with feet parallel to each other then turned out. This will change, slightly, the muscles being engaged making you a more well-rounded climber.