The film casting process is widely used to produce polymer film: a molten polymer is extruded through a flat die, then stretched in air and cooled on a chill roll. This study is devoted to the extensional flow between the die and the chill roll. The film shows a lateral neck-in as well as an inhomogeneous decrease of the thickness. An isothermal and Newtonian membrane model, constituted of an elastic-like equation for velocity coupled to a transport equation for thickness and a free surface computation, is used. These equations are solved via the finite element method (continuous Galerkin for velocity and discontinuous Galerkin for thickness). Both tracking and capturing strategies are used to determine the position of the free surface (lateral neck-in). The influence of the processing parameters (Draw ratio and Aspect ratio) on the film geometry is first determined. The onset of the Draw Resonance instability is then studied through the dynamic response of the process to small perturbations. A critical curve splitting the processing conditions into a stable and an unstable zone is derived. It is shown, consistently, with results of a 1D model, that an increase of the air-gap between the die and the roll improves the stability of the process. Numerical results concerning periodic fluctuations of the flow in unstable conditions are compared with previous experimental results.