Rapid weight-loss and aging can often result in loose skin. One of the most difficult areas to firm up is the back of the arm. Exercising the triceps muscle on the back of the arm can help get rid of those flabby upper arms that many people call “bat wings.” Start now with regular triceps exercises to rid yourself of flabby arms in time for short sleeve spring clothing. You will need some elastic exercise bands and a set of 2 pound to 5 pound dumbbells. See a doctor before beginning arm exercises if you have joint problems, such as arthritis, hand injury or an injured rotator cuff in the shoulder. Start slowly and rest a full day between exercising your arms. You may experience some muscle soreness after the first day or two of exercise, but this is normal. Stop exercising if you experience pain or notice any swelling and see a doctor. Pain is an indication of injury. To avoid injury and excess muscle soreness, seek the guidance of a personal fitness trainer and start slowly. 

Dumbbell tricep extensions can be done while sitting or standing. Grasp a dumbbell with both hands. Raise your arms over your head and then bend your elbows to lower the dumbbell behind your head. Lower the dumbbell until you feel your triceps muscle begin to stretch. Hold this position for 5 seconds and then bring the dumbbell up over your head again. Hold it for 3 seconds and then repeat the exercise by lowering the dumbbell behind your head again. Do a set of 5 to 10 repetitions. Stop when your arms begin to feel weak. 

Use a chair or a bench to perform triceps dips. Stand in front of a sturdy chair or an exercise bench. Turn your back to the chair and lower your body to place your hands, palms down on the seat of the chair or bench. Your fingers should be facing forward. Bend your knees until your legs are perpendicular to the floor at a 90 degree angle. Keep your elbows close to your body and bend your elbows as you lower your body.. You should feel your tricep muscles tighten. Hold the position for a 5 to 10 seconds. Straighten your elbows to raise your body up and hold for another 5 to 10 seconds. 

The traditional push-up is one of the most effective exercises for the tricep muscles. It also works your abdominal muscles, your chest, back, shoulders, legs and glutes. Beginners should do push-ups with their knees on the floor instead of stretching out their legs. Rest your weight on your knees and hands. Straighten your body so that your head, neck and back form a straight line. Place your palms under your shoulders with your fingers pointing forward. Slowly lower your upper body toward the floor by bending your elbows. Lower your body until your face is about 2 to 3 inches off the floor or as low as you can comfortably go. Hold the position for 2 seconds and then straighten your elbows to push your body back up.