An exact solution of the problem of designing an airfoil with a prescribed velocity distribution on the suction surface in a given uniform flow of an incompressible perfect liquid is obtained by replacing the boundary of the airfoil by vortices. By this device, a method of solution is developed, which is applicable both to isolated airfoils and to airfoils in cascade. The conformal transformation of the designed airfoil into a circle can then be obtained and the velocity distribution at any angle of attack computed. Numerical illustrations of the method are given for the airfoil in cascade.