A catheter for use in vasculature or other lumen within body structures includes a shaft formed from an elongated polymeric flexible tube. A metallic tube may be bound to the distal end of this tube. A thinner, more flexible tube may be attached to the distal end of a metallic tube. The two plastic tubes, together with any metallic tube define a lumen for providing communication with an angioplasty balloon or with a body lumen at the distal end of the catheter. A catheter may include a core member to facilitate moving the catheter through a lumen, and to reduce the likelihood that the catheter will kink or bend improperly. This metallic core member extends from the hub to some point distal on the catheter, and may extend to the distal tip of the catheter. The distal end of a catheter balloon may be secured to the core member during manufacture of the catheter. The core member has a zigzagged or helix shape at the proximal end which is friction fit into the hub lumen, and may have a pointed tip that embeds in the hub inner wall. During manufacture, the core member can be secured within the hub with reduced reliance on adhesives or molding of the core member within the hub body. The core member may be secured within the hub by being press fit into the hub lumen. The catheter is more easily manufactured, and has an increased volume and reduced obstruction by adhesive in comparison with other methods of securing the core member.