Diaphragm’s Role in Breathing. When the diaphragm contracts and moves lower, the chest cavity enlarges, reducing the pressure inside the lungs. To equalize the pressure, air enters the lungs. When the diaphragm relaxes and moves back up, the elasticity of the lungs and chest wall pushes air out of the lungs. The lungs have no skeletal muscles of their own. The work of breathing is done by the diaphragm, the muscles between the ribs (intercostal muscles), the muscles in the neck, and the abdominal muscles.