Solving the two-dimensional reduced Navier-Stokes equation for laminar flowing, shear-thinning polymer melts requires numerical calculation methods. In this study, based on the finite difference method, a 2D model for the calculation of the fully developed laminar flow in the screw channel of a melt extruder is presented. The model is linked to the constitutive equation of the General Newtonian Fluids (GNF) by the stress tensor, which allows the calculation with all material models summarized in this model family. Due to the two-dimensional structure of the model, an adjustment is done for the mass flow calculation. For this purpose, on the one hand the real cross-sectional area of the screw channel and on the other hand the velocity field of a superimposed Couette-Poiseuille flow in the rectangular channel for ideal Newtonian fluids, introduced by Rowell and Finlayson, are used. In order to determine the accuracy of the model, a parameter study is carried out in which three independent parameters, the pitch to screw diameter ratio, the channel width to height ratio and the flow exponent are varied and pressure-throughput characteristics are calculated for the range 0 < πp < 1.0. These are then compared with the results from CFD simulations. For the comparative investigations, the power law according to Ostwald and de Waele is used