A process for tunneling in tissue to install catheters and the like includes insertion of a hollow needle through the skin and, exiting from the skin as limited by the length of the needle or the catheter to be installed. A suture is then fed through the needle after which pulling tip of diameter approximately the same as the catheter to be installed, is selected and the suture attached to the distal end of the pulling tip. The catheter is then fastened to the proximal end of the pulling tip and the free end of the suture pulled to pull the catheter through the tunnel defined by the suture. The needle and suture may be inserted successively a number of times if a longer catheter is to be installed and the pulling tip and catheter pulled through the tissue. A similar procedure may be implemented using a solid needle with a swaged-on suture.