A process for making a reinforced tubular product, especially a catheter, in a single extrusion step. A reinforcing member is heated when applied to an extruded thermoplastic catheter body of about its finished size which is softened by heating while tensioning the reinforcing member to control the surface deformation or penetration of the catheter wall by the reinforcing member to produce an irregular surface contour on the catheter body. The catheter body is then smoothed in a sizing die burying the reinforcement to form the finished product. The heating step may be in addition to or substituted by a curing step when a thermosetting or crosslinking material is used for the body. The reinforcement may be braid, or a helical wrap of one or more members applied at one or more controlled angles relative to the axis of the catheter to control the strength and torque transmission efficiency of the catheter. The process is particularly adapted to making a catheter having its reinforcement interrupted to provide a unitary non-reinforced distal tip. By this process, the radial location of the reinforcement in the wall of the catheter is easily controlled according to the material of the body, the heating conditions, and the tension on the reinforcing member. Multiple extrusions to form a reinforced catheter body are thus not required.