The Push Up

The Push Up
Not just an arm & chest fact, hardly even.  
The Push Up, done correctly, should utilise the gluts; abs; obliques & deep core muscles for trunk stability.  It should be a smooth, controlled movement.  
The inability to perform a good, strong pushup could be a sign of trunk instability.
Here's an example of a regression for the traditional Push Up, done on the knees.  If this is still too difficult to do with good form then a further regression is necessary and extra work is needed to improve core stability.  A good further regression is using a fitball against the wall in order to strengthen the Push Up position.

Look out for a further post on the Fitball Push Up.