This article presents a design optimization method for maximizing lift without increasing the drag of multielement airfoils at takeoff and landing configurations. It uses an incompressible Navier-Stokes dow solver (INS2D), a chimera overlaid grid system (PEGSUS), and a constrained numerical optimizer (DOT). Aerodynamic sensitivity derivatives are obtained using finite differencing. The method is first validated with single-clement airfoil designs and then applied to three-element airfoil designs. Reliable design results are obtained at reasonable costs. Results demonstrate that numerical optimization fan be an attractive design tool for the development of multielement high-lift systems.