A dual-lumen catheter comprises an elongated cylindrical tube made of silicone and having an internal septum extending along the length thereof to form a pair of longitudinal lumens. A hollow conical tip is formed on the distal end of the tube with the outside surface of the conical tip merging smoothly with the outside surface of the tube, and the inside surface of the conical tip merging smoothly with the inside surface of one of the lumens.
The distal end of the other lumen is longitudinally spaced from the distal end of the tip. A reinforcing member is located inside the tube and extends along the length of the tube. The reinforcing member is made of a material which is substantially stiffer than the material of the tube so that the catheter can be advanced against a resistance by the applications of force to the proximal end of the catheter.