To better understand the necking phenomenon in the drawing processes of fibers, strain distributions during the drawing processes have been analyzed. For simplicity, one-dimensional incompressible steady flow at a constant temperature was assumed. Both quasi-static and dynamic models were considered. To describe mechanical properties of solid polymers, non-linear visco-plasticity material properties were assumed suing hardening and rate-sensitive equation of the power law type. The effects of various parameters on the neck formation were mathematically analyzed. As material property parameters, strain-hardening parameter, visco-elastic coefficient and strain-rate sensitivity were considered and, for process parameters, the drawing ratio and the process length were considered. It was fond that rate-insensitive materials do not reach a steady state flow and the rate-sensitivity plays a key role in obtaining a steady flow. Also, the neck formation is mainly affected by material properties and the strain distribution was found to be proportionally re-distributed along the process by the factor of the total length change, especially for the quasi-static model.