This research applies design optimization techniques to structures in adhesive contact where the dominant adhesive mechanism is the van der Waals force. Interface finite elements are developed for domains discretized by beamelements, quadrilateral elements or triangular shell elements. Example analysis problems comparing finite element results to analytical solutions are presented. These examples are then optimized, where the objective is matching a force-displacement relationship and the optimization variables are the interface element energy of adhesion or the width of beam elements in the structure. Several parameter studies are conducted and discussed.