During inspiration the diaphragm is drawn down until it lies nearly flat.
INSPIRATION The intercostal muscles raise the ribs.

The diaphragm is drawn down by contraction, thus adding to the enlargement of the chest by increasing its depth.

The abdominal muscles relax and allow the stomach, liver, and other organs in the abdomen to move downward to make room for the depressed diaphragm.

This causes a vacuum in the chest.

The lungs expand to fill this vacuum and the air rushes in to fill the expanding lungs.
EXPIRATION The intercostal, and a part of the abdominal, muscles depress the ribs and lessen the chest cavity anteriorly and laterally.