A polymer-sheeting-die-design methodology is presented that integrates a simulation of the polymer melt flow and die-cavity deformation with numerical optimization to compute a die-cavity geometry capable of giving a nearly uniform exit flow rate. Both the polymer melt flow and sheeting-die deformation are analyzed with a general-purpose finite-element program. The approach includes a user-defined element that is used to evaluate the purely viscous non-Newtonian flow in a flat die. The flow analysis, which is simplified with the Hele-Shaw approximation, is coupled to a three-dimensional finite-element simulation for die deformation. In addition, shape optimization of a polymer sheeting die is performed by the incorporation of the coupled analyses in our constrained optimization algorithm. A sample problem is discussed to illustrate the die-design methodology. (c) 2006 Wiley Periodicals, Inc.