Balls have been used for many years in physical therapy and for good reason. Just sitting on the ball places the spine in neutral alignment (why they’re often used as desk chairs) and call into action all muscles of the core or torso, referred to as the “corset” muscles -abdominals, obliques and back.
The following are examples of abdominal exercises that can be performed on a stability or exercise ball. These are written in an order of gradual progression, recommended to be practiced and accomplished in good form over a period of time.
Starting Out with Stability Ball Exercise
Sitting on the Ball
One should first experience ball training by simply sitting on the ball. With feet wide on the floor, start first by contracting the abdominals as you move your hips slightly side to side, then in small circles – one direction and then the other. This provides you with a “feel” for the ball and allows you to experience the reactive movement and balance associated with ball training.
Lowering into the Supine Incline Position
For some new exercisers, lowering into this position can be a little scary, so here are some tips to get into correct position for the supine incline exercises.
Keep your feet out wide on the floor to provide a base of stability. Place your hands on either side of the ball as you slowly walk your feet forward, keeping knees bent, and allow your hips to flex as you lower your bottom towards the floor. Stay in a somewhat upright position, only reclining slightly, and maintain constant pressure on the ball as you lower until the small of your low back (the lumbar curve) is firmly “nestled” and supported by the ball – on the side, but somewhat toward the top of the ball. 
Once you get there, your fingertips should be able to touch the floor for reassurance, if you need it.
First, get a feel for this position by contracting the abs and slightly rocking side to side. Once you feel secure, lift your arms and place them across your chest.
Stability Ball Basic Exercises
Supine Incline Pelvic Tilts
Contract the abs by focusing on pulling your belly button down and in toward the back of your spine. This should tilt your pelvis up slightly.
Tip: To check to make sure you are initiating the movement with your lower abdominals, place your hands lightly on your buttocks (glutes). If they are contracting, you are using your butt to push your hips up, rather than letting your lower abdominal region do the work.
Supine Incline Curl
Begin with your arms across your chest. Take one hand, make a fist and place it between your chin and chest. This checks the alignment of your head and neck. Keeping feet and hips fixed, contract your abdominals, again pulling the belly button down and in, and slowly flex forward with your upper torso.
Tip: in this slightly reclined position, your neck muscles may begin to fatigue. The arm position across the chest decreases the load of the curl and helps to strengthen the neck muscles that support the head. Once you begin to feel fatigue in the neck, you can take one arm up and place the hand on your upper back between the shoulders to create an arm cradle to help support the weight of your head.
Supine Incline Double Crunch
Contract the abs, belly button down and in, and perform an upper region curl at the same time as your perform a lower region pelvic tilt.
Supine Incline Oblique Curl
Keeping the feet and hips in a fixed position, contract the abs (as always – belly button down and in!) flexing forward slightly, then rotate – ribcage to opposite hip.
Tip: Reach the hand toward the inside of the opposite knee. The hand doesn’t necessarily have to touch the inside of the knee, but this directional line closely approximates the insertion points of the muscles of the obliques.