The purpose of this paper is to develop a Boundary Element Based Method (BEM) for determining the steady potential about two and three dimensional airfoil. The numerical investigation of NACA 0012 airfoil with using Boundary Element Method is utilized. Two different physical problems of the NACA 0012 airfoil are examined: potential flow around airfoil in an unbounded fluid and potential flow prediction with ground effect. Computation of potential flow around the airfoil is investigated by the mixed constant strength source and constant strength dipole based panel method. Boundary Element Code is written in FORTRAN. To check the accuracy of the 2D boundary element based code, the validation studies are carried out by comparing the present results obtained for the NACA 0012 airfoil from the XFoil and other published simulation results. 3D results are also evaluating with the available experimental and other numerical simulation results. The numerical outcomes are examined in terms of pressure distribution and lifting force on the foil.