A discrete vortex model is introduced in the calculation of the starting flows past a two-dimensional elliptic airfoil oscillating in pitch at large incidences. The potential flow past an obstacle is represented by a fixed number of bound vortices distributed along the surface and the viscous wake by an increasing number of free vortices, which are shed from the leading and trailing edges with a regular time interval and convected downstream under the action of the free stream velocity and the vortex-induced velocity. Every time stage of the calculated wake is visualized by means of point vortex plots and streamline tracings. In parallel, the instantaneous hydrodynamic loads exerted on the oscillating airfoil are estimated by using the Blasius formulae for the unsteady regime. The tested experimental parameters are the reduced pitching frequency ranging between 0.1 and 1.0 and the amplitude of oscillation between 7°and 15°. The mean incidence is fixed at 30°and the initial incidence at the minimals. Some comparison is made with the purely experimental streamlines presented in the first report.