A sheath for producing a fully sealed access to the interior of a vessel of an animal or human body comprises a base sheath having a tubular body defining a pass-through channel. The base sheath is adapted to be inserted into the vessel through a vessel aperture. A wall of the tubular body of the base sheath has a through channel. This channel extends in the wall from the distal end towards the proximal end. The channel can be present separately from the pass-through channel of the base sheath or can form a sideways extension of the pass-through channel, at least at the distal end. Such through channel is adapted to conduct blood from the vessel to the proximal end of the sheath when the sheath has been inserted into a vessel.