A theoretical study of the film casting process has been carried out. In this industrial process, a molten polymer is extruded through a flat die, then stretched in air and cooled on a chill roll, This involves mainly an extensional flow. Between the die and tile chill roll, thick edges are formed and a neck-in phenomenon is observed, Above a critical take-up speed, a drawing instability, known as draw resonance, may occur. In this paper, a one-dimensional model adapted from the classical model of the fiber spinning is developed (for a Newtonian or a Maxwell fluid), The influence of the processing parameters (draw ratio, Deborah number, and aspect ratio) on geometry of the lateral free surface (the so-called neck-in phenomenon) is studied, An unattainable zone very similar to the one encountered in fiber spinning is predicted, which only slightly depends on the stretching geometry (initial film width and stretching distance), The onset of draw resonance is studied through the linear stability method. A stability zone, depending on the geometry of the process, the elasticity of tile polymer, and the draw ratio, has been obtained. This instability is observed with simultaneous width and thickness film variations. It is proved Chat the aspect ratio (stretching distance divided by die width) has a strong influence on the onset of the draw resonance instability.