A catheter has a main portion made from an elongated tube and a soft tip that has softer flexural properties than the tube. The tip is affixed to the distal end of the tube. A reinforcement member is intermittently embedded in the body of the tube to provide kink and shear stress resistance as well as enhanced columnar strength and torque-ability to the catheter. With the flexible soft tip, the catheter is diverted when it meets an obstacle inside the patient to prevent the catheter from harming the patient. Another exemplar soft tip catheter is a one-piece elongated catheter with its distal portion selectively notched. A reinforcement member may be embedded along the length of the one-piece catheter or only along the main body portion. The notch at the distal portion may be a spiral cut or a number of ring cuts, with possibly different pitch, width and cut depth.