A viscoelastic model for PET cast film extrusion is developed on the basis of some important assumptions: constant width, vertical film, isothermal regime, Maxwell＇s constitutive equation. The general model is non-stationary, but it can be first used to cope with steady-state extrusion, which makes it possible to introduce the concept of ＇＇unattainable region＇＇, as in fiber spinning. Then the dynamic responses to random or sinusoidal fluctuations of the chill-roll velocity are analyzed. The predictions of the thickness response are in good agreement with experimental observations.