Melt blowing is a common process for the production of polymer fibers, but its effectiveness can be greatly influenced by the occurrence of fiber whipping. This paper reports the results of a systematic parametric study aimed at elucidating the factors that determine the onset of whipping in the melt blowing process. A quasi-one-dimensional model developed by Yarin and co-workers [J. Appl. Phys. 108 (2010) 034913] is analyzed in detail and extended to consider the influence of different constitutive models. It is found that whipping requires sufficiently large levels of inertia in the fiber and air, as well as a strong inlet perturbation. Strong longitudinal stresses along the jet axis are required too, although elasticity is not necessary. Also essential are a drag force that varies along the fiber length, and an air velocity that decreases in magnitude away from the fiber centerline. Comparison of results from several different constitutive models suggests that melt inertia rather than melt rheology is the more dominant factor in controlling fiber shapes. The results of the present work are expected to be helpful for the development of more quantitatively accurate models of the melt blowing process. (C) 2012 Elsevier B.V. All rights reserved.