This paper presents a new numerical algorithm for 2D nonisothermal time-stepping simulations of a nonlinear viscoelastic cast film process. A significant contribution of the algorithm is that an updated Lagrangian description of motion is employed, as opposed to the more conventional Eulerian description generally used for continuous polymer processing simulations. Furthermore, use is made of a Perzyna-type constitutive equation, which is different from what is usually employed for molten polymers. The constitutive equation accommodates viscoelasticity, extensional thinning/thickening, and strain-hardening. This new numerical algorithm can find the steady-state film properties, and it can predict the onset of instability by observing draw resonance. The critical draw ratio is determined from the response problem, which means that the mathematical complications of the more common linear stability analysis are avoided. In terms of the stability of the film, it was observed that stability is decreased by extensional thinning, strain-hardening, and higher relaxation times, and stability is increased by higher heat transfer coefficients and higher ratios of air-gap length to die width.