Thin-walled plastic screw caps are made by a two-step method: the first step is to make, by injection molding, a thin-walled plastic cup having an smooth unthreaded side wall, then to hold this cup firmly against axial movement while inserting into it, by axial movement only, a threaded mandrel, while subjecting the mandrel to ultra-sonic vibration, which causes the cup to conform to the threads on the mandrel without any pressure being applied external to the cup, so that when the mandrel is fully seated in the cup, the latter hugs the mandrel and conforms to the thread of the mandrel, thus producing a threaded cup closely hugging the mandrel. The cup is then stripped from the mandrel by rotating a friction wheel against the cup in the proper direction to unscrew the cup from the mandrel. Alternatively, instead of ultra-sonic vibration, external air pressure and heat may be used to make the thin-walled cup conform to the thread of the mandrel.