Film casting process to produce thin polymer films or membranes has several defects during its operation. Typical defects are known as neck-in/edge-bead phenomena and draw resonance instability. These have been frequently observed through film casting experiments with various polymers and process conditions and also theoretically elucidated by simulations. In the theoretical considerations, higher-order (i.e., 2-D or 3-D) simulation would be required to accurately describe the above defects in this system. Especially, analyzing the draw resonance instability, characterized by the periodic oscillations of state variables beyond onsets, is still challenging. In this study, the stability analysis in two-dimensional film casting system for viscoealstic fluids has been scrutinized employing a transfer function theory. This approach was first initiated by Kase and Araki in the fiber spinning process with power-law fluids, reporting analytic solutions for stability criteria. We tried to apply this method to the more complex extensional deformation system, i.e., film casting process. Changing the boundary condition at take-up position from constant speed to constant force (always stable boundary condition), resulting response profiles have been solved using numerical Laplace transfer and finally the relation between the response and the stability has been established. Furthermore, the frequency response patterns could be simultaneously obtained from the response data. In the frequency response analysis, amplitude ratios on whole frequency domain (0-1000/s) have been directly and efficiently determined from one response data containing take-up speed and area variables.