A catheter arrangement including a main tubing containing a radially expandable liner and a member for moving the liner out of the tubing while the tubing is in a blood vessel. Once out of the tubing, the liner expands radially outwardly into engagement with the blood vessel wall. The liner is a tube of woven plastic strands, and the moving member may be a secondary tube within the main tubing. The tubing or liner, or both, may carry a metal element for use as an X-ray marker. A smooth plastic nose cone is carried by the distal end of the main tubing, the nose cone being openable to permit ejection of the liner from the tubing.