The Archer Push-Up is a great exercise for the core and stabilising muscles, as well as for the chest, shoulders and arms. The Archer Push-Up is also a great exercise to build enough strength to be able to perform Single Arm Push-Ups.
The Archer Push-Up is an excellent exercise to improve shoulder stability, and straight arm strength whilst tying in the core when working the chest and arms.
1. Position your hands on the floor as wide as possible. If you can, keep your legs together, if you need a little extra support go wider with your feet. Make sure you core, abs and glutes are under tension. (See Fig. 1)
2. Keeping your torso straight lower yourself slowly down to one arm. Keep the other arm straight, locked at the elbow and as far away from the body as possible. Look at the hand you’re coming away from. Think of an archers position just before he fires the bow. (See Fig. 2)
3. Keeping the arm locked and straight, engage the chest, shoulders and triceps and push back up, straightening the other arm back out.  Maintain a neutral spine throughout. Repeat the movement from point 2 on the other side.

Archer Push-Up
Fig. 1

Archer Push-Up
Fig. 2

Throughout the whole movement the body should be tense, with your abdominals drawn in and shoulders positioned back and down. Be sure to keep the arms locked at the appropriate time.