The domain of operating conditions, in which the optical fiber-drawing process is successful, is an important consideration. Such a domain is mainly determined by the stresses acting on the fiber and by the stability of the process. This paper considers an electrical resistance furnace for fiber drawing and examines conditions for process feasibility. In actual practice, it is known that only certain ranges of furnace temperature and draw speed lead to successful fiber drawing. The results obtained here show that the length of the heated zone and the furnace temperature distribution are other important parameters that can be varied to obtain a feasible process. Physical behavior close to the boundary of the feasible domain is also studied. It is found that the iterative scheme for neck-down profile determination diverges rapidly when the draw temperature is lower than that at the acceptable domain boundary due to the lack of material flow. However, the divergence rate becomes much smaller as the temperature is brought close to the domain boundary. Additional information on the profile determination as one approaches the acceptable region is obtained. It is found that it is computationally expensive and time-consuming to locate the exact boundary of the feasible drawing domain. From the results obtained, along with practical considerations of material rupture, defect concentration, and flow instability, an optimum design of a fiber-drawing system can be obtained for the best fiber quality.