Spinning of PET fibers of low elasticity at high speed, and of polypropylene (of moderate elasticity) and polystyrene (of high elasticity) under non-isothermal conditions that contain their glass transition temperature, is analyzed by means of a unique BKZ-type constitutive equation that is augmented by the appropriate form of shift factors to apply in both, the rubbery and the glassy states of amorphous polymers. This approach eliminates the necessity of tracking the glassification point by trial and error, required in attempting to match different constitutive laws across it. Predictions of velocity and temperature distribution along the PET fiber agree with available experimental data, and the predicted glass transition point of polystyrene occurs indeed at about its glass transition temperature. Comparisons of predictions to those with an inelastic constitutive equation show that they apply to PET (of low elasticity) alone.