Drawing instabilities and rupture are a serious limitation in polymer fibre and film processing. Onset of these defects depends on the processing conditions, on heat transfer, and on the rheology of the polymer even if some may be encountered for Newtonian fluids. The main part of this paper is devoted to the different forms of the draw resonance instability encountered in fibre spinning, cast-film and film blowing. The time dependent equations are presented for the simplified situation of constant width cast-film. Results of the two possible modelling strategies, linear stability analysis and direct simulation, applied to the different fibre and film processes are discussed.