A computer model has been developed to simulate the behavior of molten polymer in the melt conveying zone of extruders. This model, based on a hybrid finite difference/finite element resolution of the equations of change governing momentum and heat transfer, allows the prediction of the pressure profile while accounting for wall end effects as well as the solid bed velocity. Simulation results are compared with analytical and finite difference method results found in the literature. A fairly good agreement is obtained in the case of low density polyethylene. Numerical tests are also carried out with rigid poly(vinyl chloride) compound used for window profile extrusion. The good agreement found between the predictions and experimental measurements obtained on an industrial extruder confirms the performance of the proposed model.