A numerical simulation was performed to study the roll-up of vortex sheet behind a slender delta-wing and the evolution of vortex layer shed by a plunging airfoil using the Multhopp superconvergence scheme given in Part I. Mathematical models, which are regular in the sense of Lighthill′s lemma, were proposed to simulate the vortex sheet evolution for side-slip and roll motion of wings, and solved numerically by using the superconvergence vortex method. An approach to investigate the vortex evolution in the near wake of the oscillating airfoil was also given. Our calculations have confirmed that the approach can reasonably predict the nonlinear evolution of vortex sheet.