In this paper, a multidimensional numerical simulation has been used to investigate the creation of fine fiber by the melt-blown process. The problem involves highly complex fluid flow and convective heat transfer processes. The fine fiber is created by the use of high-velocity, obliquely impinging air jets whose high shear forces stretch a polymer extrudate in the partially fluid state. High-temperature air is used to maintain the fluidity of the polymeric material as it exits the die. The model which was developed and implemented for the simulation closely reflects the physical situation employed in the actual production of fine fibers. The actual configuration of fine fiber production is a linear array of orifices from which the partially fluid polymer emerges. The array contains inherent symmetries which enable the problem to be tractable. Notwithstanding this, the numerical simulation still required multimillions of control volumes to achieve results of practical relevance. The results of the simulation indicate that, contrary to physical intuition, the shear exerted by the airflow is relatively uniform around the circumference of a given fiber. Although the interfiber spacing is small, it does not promote unfavorable fiber-to-fiber interactions.