The panel method is used for the analysis of the potential flow around any an arbitrary complex geometry. In the thesis work we presented the theory behind panel method and verified its accuracy on an elliptical wing of an aircraft. We compared the results with analytical solutions and concluded that with the correct choice of wake modeling and surface meshing, results are accurate enough for practical engineering matters where fluid flow can be approximated as potential flow. We studied the influence of different wake geometry and concluded that for practical purposes the most effective design is when the wake leaves the trailing edge symmetrically and that its length is at least several times longer as is the wingspan.