Modeling solids conveyance in a polymer extruder is difficult because it is a highly complex process. The solids are subjected to pressure and temperature gradients from the hopper through a heated section, where it is melted into a liquid over a finite distance. The polymer material possesses shear strength, which causes an anisotropic stress distribution to exist between the down channel pressure and the normal stresses on the flights, barrel and cope. A new formulation incorporating anisotropic stress states into an isotropic model is presented. Assumptions regarding the direction of the driving force applied by the screw have been examined in addition to coupling its direction with the orientation of the barrel friction force. These assumptions allow the new model to provide increased nonlinearity and flexibility to accurately predict extruder output over wide variations with discharge pressure. A new parameter,the skew angle, is introduced in the proposed model. Predictions of extruder output for varying discharge pressures and barrel temperatures show excellent agreement with experimental data.