A medical instrument cover having an elongated, generally tubular sheath of an elastomeric material, open at both ends, configured to fit on an endoscope and defining an interior surface. A filament is attached to the interior surface of the sheath and functions to separate the sheath in an elongate direction. In this manner, the sheath is easily removed from the medical instrument which it is covering.
In a second embodiment, two strips of material located generally opposite one another are attached to the interior surface. The sheath is applied to a medical instrument such as an endoscope. When it is desired to remove the sheath from the endoscope, the strips of material are grasped and pulled along the length of the endoscope thus removing the cover from said endoscope.