In this paper, a fast Lagrangian vortex method is used tonumerically simulate the unsteady vortical flows. Discrete vortices are usedto model the vorticity generation, accumulation and transport mechanisms forunsteady separated flow fields. The velocity field is computed using ageneralized Biot-Savart formula combined with a fast summation algorithm.The discrete vortices are transported by the local velocity field and theviscosity diffusion is considered with a corrected vortex core spreadingmodel. The effectiveness of the present method was examined throughcomparing the numerical simulation of unsteady separated flows past acylinder and a NACA0012 airfoil with available experimental results.Specific results are provided for an impulsively started NACA0012 airfoil ata high angle of attack. Detailed unsteady behavior at discrete time stepsfor the early stages of the flow development as well as the fully developedflow pattern is presented and discussed.