Drawing instabilities and rupture are a serious limitation in polymer fibre and film processing. Draw resonance and fibre or film rupture depend on the processing conditions, heat transfer and on the rheology of the polymer and some of these defects may also be encountered for Newtonian fluids. This paper reviews the different instabilities observed in fibre spinning, cast-film and film blowing. The time dependent equations are presented for the simplified situation of constant width cast-film and two modelling strategies, linear stability analysis and direct simulation, are proposed and then applied to the different fibre and film processes.