© by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.A method of optimizing the geometry and position of high-lift system elements is presented. The design optimization method maximizes lift without increasing the drag of multi-element airfoils at take-off and landing configurations. It uses an incompressible Navier-Stokes flow solver, a chimera overlaid grid system, and a constrained numerical optimizer. A finite-difference method is used to obtain aerodynamic sensitivity derivatives. Optimum geometries and positions of high-lift devices are obtained at reasonable computational costs. Results demonstrate that numerical optimization can be an attractive design tool for the development of multi-element high-lift systems.