Methods of manufacturing a catheter introducer or needle assembly and needle shield are disclosed. A needle shield has a blocking object (preferably a ball) which moves from an non-shielding position to a shielding position. The catheter introducer is made by placing the blocking object into the shield and inserting the proximal end of the needle into the shield while the blocking object is in the shielding position. The catheter introducer is made using extruded polymeric tubes which may have coextruded reinforcing.