In recent years, lightweight materials have been adopted in airframe design as a means to reduce aircraft weight. These lightweight materials provide adequate strength and durability, but at the expense of reduced structural rigidity. This increase in structural flexibility leads to a significant increase in the effects of aero-elastic interaction forces and moments, which can lead to important aircraft stability and control issues. In this paper, the optimal control design of an elastically shaped aircraft that has highly flexible wings is discussed. The aircraft has the capability to actively change the wing twist and bending in flight so as to achieve a local angle of attack distribution that is optimal for the specific flight condition. The aircraft has twenty three control surfaces, distributed along the trailing edge and leading edge of each wing. A multi-objective performance index that includes an explicit drag minimization term is considered, and a static output feedback controller design is performed using this performance index. Simulation results demonstrate the optimal wing shape change trajectories as well as the validity of the designed controller in stabilizing this elastic aircraft. The drag reduction achieved using static output feedback is compared with that obtained using full state feedback.