external intercostal membrane external intercostal membrane unlike the other two intercostal muscles, the external intercostal muscle does not retain its muscular character all the way to the sternum, and so the tissue in this location is called the external intercostal membrane. external intercostal membranedetailsidentifierslatinmembrana intercostalis externata98a03.3.01.002ta21710fma10475anatomical terminology the fibers of the external intercostal muscles run downward and forward between adjacent ribs. each muscle begins posteriorly at the tubercles of the ribs and extends anteriorly to the costochondral junction, the junction between the costal cartilage and the sternal end of the rib. the muscle between the costal cartilages is replaced by a membranous layer called the external intercostal membrane. links and