There are numerous important engineering applications in which the flow is inherently unsteady but periodic. Helicopter rotors in forward flight, turbomachinery blades and cooling fans operate in unsteady flow and are constantly subjected to unsteady loads. Optimization techniques for unsteady flows are clearly needed to improve their performance. As yet there have been few efforts in this direction. One of the major reasons is the demanding computational cost associated with the calculation of unsteady flows. Nevertheless, the development of optimum shape design for two-dimensional unsteady flows using the time accurate adjoint based design approach has been pursued by Nadarajah and Jameson [2].