Extrusion is a metal forming process used extensively in industry to produce different structural, mechanical, electrical, architectural, automotive and aerospace application parts. Currently after extrusion, the rod is subjected to environmental wear due to long storage time and hence requires an additional cleaning process before further use. This cleaning process can be eliminated by extruding a polymer coated metal rod workpiece such that the polymer coating is sustained on the final product after the extrusion process. In the present research study a new upper bound analytical model is developed to predict the forces required to conduct extrusion of a polymer coated metal rod successfully. The search for the lower upper bound power functional is modeled as a non linear optimization problem. Optimizing the functional also determines the set of constraints defining the shape of rigid plastic deformation boundaries and the final coating thickness. Also an upper bound analytical model was developed to predict forces for failure of the polymer coating during the extrusion. Both the analytical models for successful and failed extrusion are compared to obtain critical die angle which can provide tooling and process design guidelines. Finite element analysis simulations were modeled using commercially available software package, ABAQUS. Predictions of FEA simulations were in good agreement with published results and with the predictions of analytical model developed in this study.