A surgical tool or applier for deploying an anastomotic ring that comprises a handle connected to an elongate shaft that terminates in an anastomotic ring deployment mechanism, which is moveable from an unactuated position to an actuated position. In order to prevent tissue from becoming trapped in the ring deployment mechanism during insertion or extraction of the tool, a sheath is adapted to cover ring deployment mechanism during insertion and extraction. The sheath is moveable with the ring deployment mechanism from the unactuated position to the actuated position. The sheath may comprise an elastomeric material, a braided thread, or another material.