Computer simulation of the pneumatic processes of fiber formation from the polymer melts is discussed. The dynamics of air-drawing of thin polymer streams in supersonic air jets formed in the Laval nozzle is presented versus the melt blowing process. In the Laval nozzle process, the air flow takes place with high Reynolds number and the k? model is used which considers kinetic energy of the air flow and the specific dissipation rate of the kinetic energy. For melt blowing, the air fields are simulated with the use of the ke turbulent model. The air velocity, temperature, and pressure distributions along the centerline of the air jets are considered in the modeling of both pneumatic processes. The air fields are predetermined at the absence of the polymer streams for several air compression values in the Laval nozzle inlet and several initial air velocities in the melt blowing process. Each polymer stream in a usual configuration of a single row of the filaments in the process is considered as non-interacting aerodynamically with other streams, and the air jet is assumed to be undisturbed by the polymer streams. Air-drawing of the polymer filaments is simulated as controlled by the distribution of air velocity, temperature, and pressure on the air jet centerline with the use of a stationary model of melt spinning in a single-, thin-filament approximation. Effects of non-linear viscoelasticity of the polymer melt subjected to fast uniaxial elongation are accounted for in the modeling. Strong influence of the air jet velocity, the melt viscosity which controls response of the polymer melt on the air-drawing forces, and the die-to-collector distance has been predicted. Influence of initial air temperature, geometry of the air die, initial velocity and temperature of the melt, extrusion orifice diameter can be also predicted from the model. The example computations concern air-drawing of isotactic polypropylene with the use of the Laval nozzle are compared with the predictions for the melt blowing process. (C) 2012 Wiley Periodicals, Inc. J Appl Polym Sci, 2012