Panel methods proved a powerful-numerical method capable for hand-ling both internal and external flows. In this paper a vortex panel method is employed for studying the potential flow over one and two-element airfoils. A second order vortex method is developed to overcome the instability found in the solution when a first order vortex method is employed. Three different methods for panelling are suggested. The effect of the number of panels is also examined. Comparison of the results obtoined by this model and the exact solution of Williams two-element airfoil proved its validity. The effects of the gap and the overlap in the case of two-element air-foil are examined.