This paper marks a first effort to develop a fundamental basis for die flow analysis and design for rubber compounds. We have accomplished a modelling of the shear viscosity function and its application to one- and two-dimensional shearing in die cross sections. There are major limitations in what we have done, much of which is apparent even in the early work of Mooney. In particular, we have not considered (i) slip phenomena on die walls, (ii) die entrance and exit pressure losses associated with converging and diverging dies, nor (iii) extrudate swell. We have an active research in our laboratories investigating these problems. In the future, we are seeking to generalize the procedures described in this paper to more complex die designs. Inclusion of entrance and exit effects and rigorous analysis of coathanger dies requires the handling of elongational flow contributions, a still unsolved problem.