Viscoelastic flow in a Buss Kneader in which the screw has both rotating and oscillating motions is simulated. Linear viscoelastic responses are considered using both the Maxwell model and the Boltzmann superposition model. Calculations are made first in a basic screw element and subsequently in Kneader screw modules where we consider leakage flows through the interrupted screw flights. Our study includes filled length variation in the crosshead screw extruder, screw characteristics of Kneader screw elements, and pressure profiles along the modular Kneader machine.