A mathematical model based on the formalism of Doufas et al. [A.K. Doufas, I.S. Dairanieh, A.J. McHugh, J. Rheol. 43 (1999) 85-109] was developed for the simulation of both low- and high-speed melt spinning including the combined effects of flow-induced crystallization (FIC), viscoelasticity, filament cooling, air drag, inertia, surface tension and gravity. Both an amorphous phase, simulated as a modified Giesekus fluid, and a semi-crystalline phase, approximated as rigid rods that grow and orient in the flow field, are coupled through the stress and momentum balance and the feedback of crystallinity to the system relaxation times. Since the onset of crystallization occurs at the equilibrium melting point, the freeze point arises naturally. The model is robust over a wide range of processing conditions and input parameters and exhibits material behavior consistent with that observed for semi-crystalline polymers under all spinning conditions. The model predicts neck-like deformation and associated strain softening in high-speed spinning, as well as the related velocity-, diameter-, temperature-, tensile stress-, apparent elongational viscosity-, orientation- and crystallinity-profiles. Calculations for the systems studied indicate that extensional softening followed almost immediately by FIC provides the primary mechanism responsible for neck formation, in agreement with experimental observations. The model provides a framework for the simulation and optimization of melt spinning involving FIC.