Abstract: In melt spinning a crystalline plastic material such as, for example, nylon 6, molten filaments discharged through the spinneret are drafted at a mathematical draft of not less than 3 and, while being so drafted in their molten state, are abruptly cooled to a temperature below -30.degree.C, whereby the microbrownian motion of the molecules in the filaments is frozen while the molecules in the filaments are retained in a specific oriented state. When the filaments in which the molecules are oriented in a fixed direction and hence the chains of molecules are in a readily stretchable state are further subjected to a stretching treatment at a temperature at which the microbrownian motion of molecules remains frozen, there are produced filaments possessed of mechanical strengths far exceeding those exhibited by filaments which are spun and stretched by the conventional method.