A method is presented for determining the two levels of instability that are associated with thin web materials traveling through process machinery. The first level of instability involves the out-of-plane buckling of expanses of web supported only by rollers at opposing ends. A method is developed using linear plate theory, which is verified by tests that show that this first level of instability can be predicted. The second level of instability involves the buckling of the web when it has taken the form of a cylindrical shell as it transits a roller. A nonlinear finite element method with strain dependent constitutive relations is developed and verified by tests to predict this second level of instability.