A model for the optimal design of a multi-stage compressor, assuming a fixed configuration of the flow-path, is presented. The absolute inlet and exit angles of the rotor, the absolute exit angle of the stator, and the relative gas densities at the inlet and exit stations of the stator, of every stage, are taken as the design variables. Analytical relations of the compressor elemental stage and the multi-stage compressor are obtained. Numerical examples are provided to illustrate the effects of various parameters on the optimal performance of the multi-stage compressor. (c) 2007 Elsevier Ltd. All rights reserved.