tendon sheath tendon sheath a tendon sheath is a layer of synovial membrane around a tendon. it permits the tendon to stretch and not adhere to the surrounding fascia. tendon sheathdetailsidentifierslatinvagina tendinisthh3.03.00.0.00028 fma76715anatomical terminology it has two layers: synovial sheath fibrous tendon sheath fibroma of the tendon sheath has been described.