The main muscles involved - chest and triceps indirectly loaded front delts, forearms, and small hand muscles, the muscles of the lower back, abs and quads.
Triceps (especially his long head) powerfully stimulated push-ups a narrow focus. The outer head of the triceps originates on the posterior surface of the humerus, but does not cross the shoulder joint. Internal head triceps begins in the middle of the humerus and mostly covered by the other two heads - some of it can be seen directly above the elbow.
The long head of the triceps begins on the scapula below the shoulder joint, and on the way down merging with other heads, crosses the elbow joint by attaching to the ulna of the forearm. Long head gets the most stress, because it simultaneously and extends the shoulder joint and ulna. The outer and inner heads of the triceps help in straightening the elbow. Accepted the position of the stop lying, soles of the feet have a very close relative to one another.