Intercostal muscles are several groups of muscles that run between the ribs, and help form and move the chest wall. The intercostal muscles are mainly involved in the mechanical aspect of breathing. These muscles help expand and shrink the size of the chest cavity to facilitate breathing. Intercostal muscles are several groups of muscles that run between the ribs, and help form and move the chest wall. The intercostal muscles are mainly involved in the mechanical aspect of breathing. These muscles help expand and shrink the size of the chest cavity to facilitate breathing.