The constitutive model for flow-induced crystallization (FIC) developed by the present authors [Doufas et al. (1999, 2000a, 2000b), Doufas and McHugh (2001)], coupling polymer microstructure (chain extension, molecular orientation, and crystallinity) with the macroscopic transport equations (mass, momentum and energy), is applied to a two-dimensional simulation of melt spinning. The model predicts the radial variation of tensile stress and microstructure driven by the radial variation of the temperature, which is caused by low polymer thermal conductivity. In the limit of infinite thermal conductivity, radially uniform profiles for the temperature and the microstructure are consistently predicted. The formation of a skin-core structure observed experimentally is also predicted, where the molecular orientation, crystallinity, and tensile stress are highest at the surface of the fiber and lowest at the centerline. The microstructure is predicted to lock in below the freeze point preserving its radial variation despite the collapse of the temperature radial variation at large distances below the spinneret. Under the conditions investigated, for both nylon and polyethylene teraphythalate systems, the cross-sectionally averaged variables do not deviate significantly from the respective uniform quantities of the one-dimensional formulation at the freeze point. We suggest that the model can be used as an optimization tool for melt spinning processes predicting the final fiber properties through the radial variation of the microstructural variables.