This paper presents a series of simulation approaches to model the mechanisms associated with the flow and breakup of a polymer melt in a new micropelletization technique. This has proven to be an alternative way of producing micropellets and powders with physical properties demanded in polymer processes such as sintering, rotomolding, injection molding, and extrusion. The new technique involves extruding a polymer melt strand through a capillary and stretching it with a stream of hot air, causing the formation of Rayleigh disturbances that lead to breakup of the strand into small particles. Experimental work has demonstrated that the viscoelastic response of the extruded thread influences the breakup process, affecting the final shape and size distribution of the particles. This work presents simulation results for the melt flow behavior that reproduces what has been observed experimentally during the breakup stage. A free surface viscoelastic solver, implemented in the OpenFOAM computational fluid dynamics software, allows visualization of viscoelastic effects on the melt as it leaves the extrusion die and meets the stream of air. Modeling of the viscoelastic fluid flow in this process is intended to serve as a tool for process control and understanding of influential factors in the development of micropellets, for a range of materials and process conditions.