We present a general model for a multi-step regenerative irreversible Brayton cycle on thermodynamic basis. The model incorporates an arbitrary number or turbines and compressors with reheating and intercooling intermediate processes. We consider several internal and external irreversibility sources that include losses in the non-isentropic turbines and compressors, pressure drops in the heat input and heat release, irreversibilities in the regenerative heat exchanger, heat-leak through the plant to the ambient and non-ideal couplings with the external constant-temperature heat reservoirs. The general equations for power output and efficiency depend on a reasonable low number of parameters, with a clear physical meaning, that account for cycle design and geometry, and for the characterization of irreversibilities. From this general model several results found in the literature could be considered as particular or limit cases. Moreover, we explicitly compare our theoretical results with computer simulation results in the literature for particular plant arrangements where the number of turbines and compressors is not the same. Also, we analyze the maximum power and maximum efficiency working regimes in terms of internal and external irreversibilities. (C) 2010 Elsevier Ltd. All rights reserved.