A new mathematical model has been developed to analyze the entire flow field of a single screw extruder under steady-state conditions. Intended as a rational design tool for practising engineers in the polymer processing industry, the model contains no partial differential equations and hence does not require the use of numerical solution techniques. To achieve generality, a generic approach is proposed and has been adopted in the derivation of governing algebraic equations from general conservation laws covering channel geometry, polymer flow speed, equivalent radius in a pipe, material properties, power consumption and heat transfer. The model makes no use of empirical factors or correlation. The validity of the new model has been assessed by comparison with published experimental results. Good agreement was achieved with respect to its ability to predict (a) the solid-bed width profile; (b) the axial pressure profile and (c) the temperature and pressure of the melt pool at the extruder exit. Furthermore, the model can predict other information including the solid-bed velocity in the axial direction and the power consumption. The work has demonstrated the potential of a fast track approach to designing helical extruder screws, while maintaining a level of accuracy comparable with more complex 3D models but without the penalty of computational efforts.