Plank is a well-known exercise that we see in both Pilates and yoga.
It is one of the most popular exercises for developing core strength
and stability.
While Plank really targets the abdominals and shoulder stability, you
will find that plank is an excellent way to get a full body challenge.
In order to do Plank properly there must be integration of all the
core stabilization muscles. The arms, glutes, and legs are active as
well.
Plank can look like the "up" of a regular push up. But, in most cases,
a regular push up entails much more strain in the upper body -
especially in the shoulders and neck - than plank in Pilates or yoga.
You may want to begin with a modified version of Plank and work up to
the full version, especially if you are weak in the upper body or have
neck strain issues. Please see the plank preparation exercise.
You will know you're doing plank well when you have good form, feel
your center working, and have good shoulder stabilization yet are not
incredibly rigid.

Nota : The name "plank" comes from yoga.
Pilates has traditionally referred to this move as "front support",
but that seems to be giving way to the more commonly used term, plank.

Start Position
Begin on your knees. Place your hands on the floor in front of you,
fingers pointing straight ahead. Your arms are straight and elbows are
not locked.
Engage your abdominals and lengthen your spine, extending energy
through the top of your head and down through your tailbone.
Lean forward to put your weight on your hands. Align your shoulders
directly over your wrists.

Workout
With your abdominals lifted, extend your legs straight behind you.
Keep them together and send energy through your heels.
Your toes are curled under so that some weight is on the balls of your
feet.
Without over-tightening, activate your legs (especially your
hamstrings) and bring them together, emphasizing the center line.
Similarly, activate but do not clench your glutes (butt muscles) -
think of pulling your sit bones together.
Breathe deeply, allowing the breath to expand into your lower ribs and
back.
Hold your position for three to five breaths.
Take a break and repeat up to five times.

Plank Preparation Exercise / Modification
Place your forearms, parallel to each other, on the floor. Many people
find that making a fist with the hands is helpful.
Your shoulders should be directly over your elbows.

Tips
Your body is in a straight line from the ears, through the shoulders
and hips, and to the heels. Do not arch or sag.
Keep the abdominals lifted throughout this exercise. You want to
engage the muscles of the pelvic floor as well.
Put some space between the base of your scull and your neck.
Keep your shoulders dropped.
Breathe deeply into the sides and back.
If you start to shake, release the pose, breathe, and start again.

Benefits
Strengthens the abdominal muscles, the pelvic floor, the gluteal
muscles, the legs and the arms.

See the picture here : http://www.style-pilates.com/pilates-plank-pose.html