Flow of polymer melts in a screw extruder is analyzed using a viscoelastic model of a modified second-order fluid. The equations of motion are solved numerically by modifying the computational procedure advanced by Fredrickson, and the calculated extruder throughputs at various operating conditions are found to be in reasonable agreement with the experimentally observed values. Furthermore, the computational algorithm developed in the present study provides the profiles of shear rates and melt viscosity in the screw channel.