The operating conditions of a solid oxide fuel cell (SOFC) system that result in maximum efficiency needs to be studied by considering the whole closed circuit system because operating at maximum cell efficiency may not lead to maximum system efficiency. In this paper, this study is performed with the aid of a comprehensive steady state model of the SOFC, the after-burner, and the heat exchangers. In order to account for the large irreversibilities, the SOFC model is derived by the application of the second law of thermodynamics to the fuel cell control volumes. The SOFC system efficiency is maximized by employing a recursive algorithm with two cascaded optimization loops, which also gives the corresponding cell operating conditions. Complex control laws are required for controlling the SOFC system for maximum efficiency. On the other hand, it is found that an appropriately chosen constant fuel utilization operation closely approximates the maximum efficiency operation of the fuel cell in its operating range.