In this paper an inverse design method is presented which couples a Navier-Stokes flow solver and a numerical optimization algorithm. The design method generates a compressor cascade, producing a specified surface pressure distribution at a transonic speed. A least-square optimization technique is used to minimize pressure discrepancies between the target and designed cascades. In order to represent the nonlinear, rotational and viscous physics of transonic flows, Navier-Stokes equations are used to predict the flow field. Sensitivity derivatives are obtained using finite differencing. Effects of different design variables on the performance of design optimization are evaluated. Sensitivities are calculated on parallel processors to reduce the computational cost. © 2000 The American Institute of Aeronautics and Astronautics Inc. All rights reserved.