supraspinous fascia supraspinous fascia the supraspinous fascia completes the osseofibrous case in which the supraspinatus muscle is contained; it affords attachment, by its deep surface, to some of the fibers of the muscle. supraspinous fasciamuscles on the dorsum of the scapula, and the triceps brachii. (fascia not labeled, but supraspinatus visible at top right.)detailsidentifierslatinfascia supraspinatata98a04.6.02.007ta22538fma38353anatomical terminology it is thick medially, but thinner laterally under the coracoacromial ligament.