In the accompanying article, Part I, we have described the basic mechanism of chaotic mixings due to a new ＇＇Chaos Screw＇＇ in single-screw extrusion processes, and presented experimental evidence of the chaotic mixing in a single-screw extruder with a typical Chaos Screw installed. The:present article, Part II, will be focused on the numerical investigations of the chaotic flows via the Chaos Screw in a single-screw extruder. The three-dimensional velocity fields in both the no-barrier and barrier regions were separately calculated via a finite element analysis of the quasi-three-dimensional flow in each region, and were subsequently used in the numerical simulations of chaotic flow behaviors. Extensive numerical simulation results will be presented in terms of particle trajectories, Poincare sections, and mixing patterns for several dimensionless parameters. It was found that invariant manifolds obtained by numerical simulations were in good agreement with those from experiments.