The traditional method of mathematical modeling of the die flows treats the die as a stand alone tool which is independent of the extrusion conditions which feed the polymer melt into the die. Here, we demonstrate that especially under the conditions where a breaker plate is not used the flow and the deformation which occur in the die are dependent on the prevailing velocity and the stress conditions of the fluid at the extruder which feeds the die. A finite element method based technique is used to solve the conservation equations using a mesh which covers both; the die and the rotating conical screw tips of the extruder. The presented methodologies provide a more realistic representation of the thermo-mechanical history experienced by the polymer melt or structured fluids including emulsions or suspensions in the die and thus provide better tools for die design and process optimization. The results also suggest that significant improvements in die design and hence die performance could ensue by using the geometry of the screw tips, the distance between the screw tips and the die and the rotational screw speed as additional parameters for design and optimization.