A typical integrated-planar solid oxide fuel cell (IP-SOFC) consists of modules with series connected electrochemical cells printed on their outer surfaces. Oxygen is supplied to the cathodes from air flowing over the outside of the module and hydrogen diffuses from the internal fuel channels to the anodes through the porous module support structure. The IP-SOFC is intended for use in medium scale stationary power applications, and such a system will use a fuel cell stack containing many thousands of modules housed inside a pressure vessel. For certain purposes, the geometry of this stack can be adequately described using a computational domain that considers just two modules. A computer code has been developed to simulate the many physical and chemical processes occurring within the stack, including fluid flow, heat transfer, water gas shift, and electrochemical reactions. The simulation results show how the performance of the IP-SOFC stack is strongly affected by these physical processes, the geometry of the stack, and the operating conditions. The temperature distribution, which is difficult to predict using a less realistic geometric model, is almost uniform within each fuel channel and rises steadily in the air flow direction. The shift reaction, which is catalyzed by the anodes, is of great importance, and as the fuel flow becomes depleted of hydrogen it enables the electrochemical cells to make increasing use of carbon monoxide. Overall it was found that the operating voltage produced by the fuel cells is typically and the component efficiency, the ratio of the actual power output to the maximum available from the fuels consumed, is around 59%.