© 1997, American Institute of Aeronautics and Astronautics, Inc.An aerodynamic design method is presented that couples flow analysis and numerical optimization to improve the aerodynamic performance of a turbomachinery blade subject to specified design objectives and constraints. The flow field prediction is based on the Euler equations in order to represent the nonlinear rotational physics of transonic flows. The sensitivity analysis that measures the response of the flow with respect to a geometry perturbation is calculated by finite differencing. A special care is given to improve the accuracy of sensitivity derivatives in terms of truncation and condition errors. Numerical optimization can find a better design even with strict design constraints imposed. The method is demonstrated with several examples.