A polymer sheeting die design methodology is presented, which integrates finite element flow simulations, numerical optimization, and design sensitivity analyses to compute die cavity geometries capable of giving a near-uniform exit velocity. This work extends earlier die design methods to include generalized Newtonian fluid (GNF) models that represent the shear-thinning behavior of polymer melt. Melt flow computations and design sensitivity analyses are provided using the generalized Hele-Shaw flow approximation with isothermal powerlaw, Carreau-Yasuda, Cross, Ellis, and Bingham fluid models. The nonlinear equations for die cavity pressure are solved using the Newton-Raphson iteration method and design sensitivities are derived with the adjoint variable method. The die design method is applied to an industrial coat hanger die, in which a design parameterization is defined that allows for an arbitrary gap height distribution in the manifold of the die. In addition, die performance is assessed and compared for power-law and Carreau-Yasuda fluid flow over a range of die operating conditions. Pareto optimal die designs are also considered in this study. (c) 2005 Society of Plastics Engineers.