Turbine rotors and compressor rotors are subject to centrifugal and thermal loads. These loads increase proportionally with tip speed and gas temperature respectively. Additionally, rotor weight must be decreased to improve rotor dynamics and to restrict bearing load. Thus, an optimum design technique is required which offers the lightest possible wheel shape under the stress limit restriction. This paper introduces an optimum design system developed for turbo-machinery rotors, and discusses several applications. The sequential linear programming method is used in the optimizing process, and unsteady state thermal analyses of variable thickness wheels are performed using the numerical analysis method of multi-ring model. Centrifugal and thermal stress analyses of these wheels are performed using Donath's method with same multi-ring model. This optimum design program is applied to the design of axial flow compressor wheels. Finally, the validity of these applied results are confirmed by the transient thermal and stress analyses using the Finite Element Method.