An analytical model has been developed which predicts the stack stiffness of multiple layers of films with rough surfaces. Film surfaces are approximated by asperity distributions measured using commercially available equipment. Comparisons were made with stack compression measurements made in a vacuum. It was found that measurements taken in a vacuum were quite different from those taken in air. Approximate correlations are included for PET films. The results are suitable for approximating the radial elastic modulus in rolls of film.