SUMMARYA polymer processing design methodology is presented which can be used to improve the production of plastic components manufactured via extrusion and injection molding processes. The design method combines polymer process modelling, design sensitivity analysis and numerical optimization. It is applicable to systems with creeping ow of purely viscous non-Newtonian uids through thin cavities where the lubrication approximation may be applied. An analysis and an adjoint design sensitivity analysis are presented for the steady-state coupled system which describes the pressure and residence time distributions in sheeting dies. The resulting methodology is then used to deÿne the optimal die cavity shape and relevant process parameters in a sheeting die design example. A second example considers tooling and process design for the polymer injection molding process. A coupled transient mold ÿlling analysis and design sensitivity analysis based on the direct di erentiation method are developed where attention is given to describing the location of the gates in the mold cavity. The latter is illustrated through the process design of a plastic automotive component.