There are eleven paired internal intercostal muscles, one on either side of the rib cage.
The internal intercostal mm. commence anteriorly at the sternum in the spaces between the cartilages of the true ribs and at the anterior ends of the cartilages of the false ribs. The internal intercostal mm. extend posteriorly as far as the angles of the ribs. From there, they continue to the vertebral column as thin membranes (the posterior intercostal membranes).
Each internal intercostal m. arises from a ridge on the inner surface of the rib and corresponding costal cartilage, and is inserted into the inferior border of the rib above.
The internal intercostal mm. fibers are perpendicular to the external intercostal mm. fibers. The internal intercostal mm. fibers are directed obliquely upward and laterally on the front of the thorax (the analogy is "hands over the heart" - if you cross your hands over your chest, your fingers align with the orientation of the internal intercostal mm. fibers).
The internal intercostal mm. are muscles of expiration. During forceful exhalation (e.g., coughing or during exercise), the interosseous portions of the internal intercostal mm. (the part of the muscles that is between the bony portions of the ribs) depresses and retracts the ribs, compressing the thoracic cavity and expelling air. The internal intercostal mm. are not used in relaxed expiration.
The images above show a lateral view of the right half of a rib cage, with the anterior direction to the right of each image.