Abstract: In the method for the manufacture of curved plastic pieces, such as brassiere underwires, the plastic pieces are formed from hot plastic material in a selected mold and are cooled to solidify the plastic material. In the improved method, a continuous thermoplastic wire in its thermoplastically formable state is coiled into a coil and simultaneously cooled thus forming turns of a solidified coil. The turns are subsequently cut along the axis of the coil over the entire length of the coil to produce the curved plastic pieces.