The understanding of the basic physical effects of viscoelasticity on drawing performances in the coating process leads to a useful approach to link the rupture of the polymer melt to critical processing conditions. In particular, we show that when solving the drawing problem in the air gap with a simple constitutive equation-like the upper convected Maxwell model-a mathematical inconsistency appears for some drawing parameters. This mathematical instability may be experimentally correlated to the occurrence of melt-rupture, giving rise to a discussion on the effect of viscoelastic properties on drawing performances. Results are given in terms of a diagram representing the maximum drawing ratio Dr with respect to the Deborah number De. A master curve, obtained form experimental results, accounts for the temperature, melt-index, air-gap height, and extrusion output dependences. The limitations of the '' universality '' of the concept are discussed later.