This paper presents a design method for two-dimensional transonic turbine blades. It couples a Navier-Stokes flow solver and a numerical optimization algorithm to improve the aerodynamic performance of transonic turbine blades subject to specified design objective and constraints. The flow field prediction is based on the Navier-Stokes equations in order to represent accurately the nonlinear, rotational and viscous physics of turbomachinery flow fields. Effects of different design variables on the performance of design optimization are evaluated. Sensitivity derivatives are obtained using finite differencing. The method is demonstrated with several examples at transonic flow conditions. © 2000 by the American Institute of Aeronautics and Astronautics. Inc. All rights reserved.