The epiglottis is a flap that is made of elastic cartilage tissue covered with a mucous membrane, attached to the entrance of the larynx. It projects obliquely upwards behind the tongue and the hyoid bone, pointing dorsally.nflammation of the epiglottis is known as epiglottitis. Epiglottitis is mainly caused by Haemophilus influenzae. A person with epiglottitis may have a fever, sore throat, difficulty swallowing, and difficulty breathing.