Targets for inertial confinement fusion shots on the National Ignition Facility typically use thin polyimide films, ~500 nm, with a coating of 25 nm of aluminum as windows that seal the laser entrance hole. Their role is to contain the hohlraum gas and minimize the extraneous infrared radiation getting in. This is necessary to control precisely the hohlraum thermal environment for layering inside the capsule with solid deuterium-tritium at 18 K. Here, we use our empirical data on the bulging behavior of these foils under various different conditions to develop models to capture the complex viscoelastic behavior of these films at both room and cryogenic temperatures. The constitutive equations derived from these models give us the ability to quantitatively specify the film’s behavior during the fielding of these targets and set the best parameters for new target designs.