Electrospinning and melt blowing are the most commonly used processes to produce microfibers from extruded polymer solution or melt. The present work deals with the dynamic modeling of the whipping instability and related processes during production of microfibers. A bead-viscoelastic element fiber model is employed in modeling three-dimensional paths of the fiber motion in the processes of electrospinning and melt blowing. The simulation results provide a reasonable comparison between these two processes and point out that the Coulomb force in electrospinning always has the function to sustain and increase the bending instability; while in the melt blowing process, whether the aerodynamic force increases the bending instability or not depends on several factors.