Epimysium The structure indicated in this diagram is the epimysium. Skeletal muscle fibres are organised into bundles, called fascicles. Each fibre within the fascicle is surrounded by connective tissue called endomysium. Surrounding each fascicle (bundle), is the perimysium. Extensions of the perimysium project into the fascicles to blend with the endomysium. Surrounding the groups of fascicles is the epimysium, which covers the outer surface of the muscle. The epimysium is composed of dense irregular connective tissue. The epimysium can extend beyond the fleshy muscle fibres to form tendons or aponeuroses, which then form attachments to the periosteum of bones.