In this work, an optimization study of the delivered power density by the solid oxide fuel cells is presented according to a thermodynamic model. The power density is defined by the current density, the Nernst potential and the three losses: concentration, activation and ohmic. A comparison between the Tafel and Butler-Volmer formulations was performed to quantify the activation loss. A program in FORTRAN language was developed locally for the resolution of the mathematical equations representing the used physical model. The obtained results show that the SOFCs power density is inversely proportional to the anode thickness, electrolyte thickness and cathode thickness. The optimum fuel water content ensures the maximum power density is 6.25%. The cell power density is proportional to the oxygen concentration in the oxidant, the operating temperature and the operating pressure. (C) 2018 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.