It is the purpose of this study to obtain solutions, which contain complete discontinuities of shock waves, of the potential equations for transonic airfoils using numerical techniques. For iterative calculations, the potential equations are transformed into a more convenient form of simultaneous equations with two variables of velocity potential and Mach number. The solutions with the complete discontinuities of shock waves satisfying Prandtle's relationship are obtained by the iterative calculations without divergencies or hight frequencies under a grid system in the physical plane. Numerical results of the present techniques and of another methods for the transonic flow over airfoil of NACA 0012 with shock wave are used as test cases of comparisons.