In this work we investigate the use of an inhomogeneous structural model which explicitly takes into account flow-induced crystallization for representing the necking phenomenon in high-speed fiber spinning. For simplicity, we have considered a one-dimensional (cross-section averaged) approximation for an isothermal system with no surface tension and air drag, with or without inertia. Flory’s approach [J. Chem. Phys.15, 397–408, (1947)] is used to predict the onset of crystallization in the spinline. After the onset of crystallization, the fiber is modeled as an inhomogeneous medium with two separate (meso) phases—one semi-crystalline and the other amorphous. The amorphous phase, before and after the onset of crystallization, is modeled as a viscoelastic fluid, represented here by the extended White–Metzner model. The semi-crystalline phase is modeled as an anelastic solid. We demonstrate neck formation for a variety of processing conditions and material property values consistent with those encountered in practice. In particular, the addition of inertial effects, which can also be important in high-speed fiber spinning, shifts but does not eliminate the window in parameter space over which the inertialess model predicts neck formation. Based on these results, we propose as a mechanism for the neck formation the structural changes within the material induced by the crystallization and the ability of the semi-crystalline phase to rapidly take up high stresses.