A system for manufacturing a catheter includes at least first and second controllable rate material feeders that feed at least first and second materials into a temperature-controlled mixer to form a compound material that varies in flexibility and/or strength with the respective first and second materials and material feed rates. An extruder extrudes the compound material onto a rotating and translating mandrel to thereby form a variable stiffness profile along a length of the catheter that depends on respective rates of rotation and translation of the mandrel.