An air-drawing model of poly-L-lactide melt under a supersonic air jet in the Laval nozzle is presented. The aerodynamic fields are computed using the k-omega model. The pneumatic process is considered based on the mathematical model of melt spinning in single-, thin-filament approximation. Simultaneous acceleration of the air and the melt within the nozzle leads to fast attenuation of the filament. Air velocity dominates velocity of the filament and results in continual air-drawing on the entire spinning line. Oriented crystallization and nonlinear viscoelasticity effects under fast uniaxial elongation of the polymer melt are considered. The filament velocity at the collector increases significantly with increasing air compression, from the values typical for high-speed melt spinning up to values by two folds higher. The increase in filament velocity is limited by the effects of online oriented crystallization at higher air compressions. Influence of the inlet air compression, melt extrusion temperature and weight-average molecular weight on the axial profiles of the melt spinning functions is discussed, as well as on the development of amorphous orientation and online oriented crystallization.