A method and apparatus for continuous drawing of fibers in the form of coiled fiber loops (e.g., polygonal or serpentine loops). The successive fiber loops are continuously laid on receiving ends of a plurality of conveyer-drawing members (CDM) [e.g., rotating threaded spindles (54) or circulating endless chains (80) and (108)] disposed about a central axis and diverged from this axis. Coiled fiber loops are conveyed along the central axis and simultaneously drawn by enlarging a circumference of the fiber loops by the CDM. The leading fiber loops are continuously taken off at delivery ends of the CDM and conveyed from the drawing apparatus at an outlet speed. Heat chambers (11) and (148) envelop at least the most part of CDM. The process can operate at low drawing speed and long drawing time typical for lab-scale experiments and equal or higher outlet speed and throughput typical for commercial drawing processes. The method can produce low-cost/high-strength/high-modulus/low-shrinkage commercial polymer fibers.