This paper presents a model and a structured procedure to optimize the internal structure of a single solid oxide fuel cell (SOFC) so that the power density is maximized. The polarization curve and power density are obtained as functions of temperature, geometry and operating parameters. The internal structure, which accounts for the thickness of the two electrodes and the electrolyte, and the flow channels geometry, has been optimized. The model is developed using a control volume approach, in which, all relevant thermal and electrochemical interactions between adjacent elements are accounted for. The effects of geometry on the compartments temperatures and reactants concentrations in the fuel cell are explored. The optimized internal structure results from optimal balances between the thickness of anode and cathode, L-3 and L-5, shoulder channel aspect ratio, L-t/L-ch, and the total number of fuel and oxidant channels, n(ch). The optima found are sharp and, therefore, important to be identified in actual SOFC design. The variations of power density in the studied ranges of L-3 and L-5, L-t/L-ch, and n(ch) were of 11, 5 and 5%, respectively, in the three-way optimization process, for the anode-supported single SOFC. Copyright (c) 2007 John Wiley & Sons, Ltd.