The forward or backward stagger angles of the kneading disks have great effects on configures of the special center region along axial length in a novel tri-screw extruder. In this paper, the flow and mixing of a nonNewtonian polyethylene in kneading disks of a tri-screw extruder were simulated using three-dimensional finite element modeling based on mesh superposition technique. Three types of kneading disks, neutral stagger, staggered 30° forward and staggered 30° reverse were considered for the tri-screw extruder. The effects of stagger angles of kneading disks on the flow pattern in the tri-screw extruder were investigated. Moreover, at different stagger angles, the dispersive and distributive mixing efficiencies in the kneading disks of the tri-screw extruder and the twin-screw extruder were calculated and compared by means of mean shear rate, stretching rates, maximal stress magnitudes, mixing index, residence time distribution (RTD) and logarithm of area stretch. It is found that increasing the stagger angles decreases the axial velocities of polymer melt in the center region for the tri-screw extruder. The staggered 30° reverse is relatively reasonable for the tri-screw extruder and neutral stagger for the twin-screw extruder for the mixing efficiency. In comparison, the kneading disks in the tri-screw extruder have higher distributive and dispersive mixing efficiencies than those in the twin-screw extruder with the same stagger angles.