One of the main limitation in producing polymer film by Cast Film extrusion or by Film Blowing is the occurrence of drawing instabilities. This phenomenon is well known since the 70ies for fiber spinning: Above a critical Draw Ratio the filament diameter presents marked periodic variations. The occurrence of this instability depends on the rheological behavior of the polymer, but also on the drawing length, the cooling intensity. In the Cast Film process, the phenomenon is more complex as it involves both the film width and the film thickness (which may become uneven during stretching). In the film blowing process the phenomenon is even more complex because of the conjunction of the Draw Ratio and the Blow-Up Ratio. Experiments in both film casting and film blowing processes will be presented. Simulation will be performed by two complementary methods. A linear stability analysis allows determining quickly the critical Draw Ratio (the critical Blow-Up Ratio) for the occurrence of the defect in simplified situations (constant film thickness through the width or along the perimeter of the film) . Direct numerical simulations allow accounting for more complex situations, but also to determine the periodic solution in unstable conditions.