This is a section of a catheter used in making a catheter assembly suitable for accessing a tissue target within the body, typically a target which is accessible through the vascular system. The catheter section uses a braided metallic reinforcing member, typically of superelastic alloy ribbon, situated within the catheter body in such a way to create a catheter having an exceptionally thin wall, controlled stiffness, high resistance to kinking, and complete recovery in vivo from kinking situations. The braid may have a single pitch or may vary in pitch along the axis of the catheter or catheter section. The braided ribbon reinforcing member typically is placed between a flexible outer tubing member and an inner tubing member to produce a catheter section which is very flexible but highly kink. resistant. The catheter sections may be used alone or in conjunction with other catheter sections either made using the concepts shown herein or made in other ways.