The shape design optimization problem can be formulated as an optimal control of a system governed by partial differential equations where the controls are on the boundary. In aerodynamics a suitable cost function is chosen according to some criteria and its minimum represents the optimal shape sought. With this method we intend to study the control of two-dimensional aeroelasticity, using an unsteady Euler model and simplified structural analysis. The research work will consist in a preliminary theoretical study which includes the derivation and analysis of the optimality problem. Then we will consider the problem of a consistent and accurate discretization of the optimality system. Subsequently we will study simple test cases to validate the algorithm and finally we will attack more realistic problems. With our approach, injecting more knowledge in the design process, it would be possible to reduce the cost of all those experimental activities put up to reduce the unknown aspects of the phenomena involved and to get to a design of higher quality.