A three-dimensional model of a methanol-fueled solid oxide fuel cell (SOFC) that sufficiently considers the rib structure to understand the effects of operating conditions on a methanol-fueled SOFC is developed. The model considers the coupling of electrochemical reactions, mass transport, heat transfer, and thermal stress. The overall performance of the methanol-fueled SOFC is investigated under the influence of operating voltage, steam-to-carbon ratio, and porosity. The results indicate that as the operating voltage increases, the overall anode switches from exothermic to endothermic, and the stress of the anode first decreases and then increases. As the steam-to-carbon ratio increases, the overall temperature of the anode decreases. However, when the steam-to-carbon ratio is less than 1, the temperature at the inlet is lower than the ambient temperature. Meanwhile, the first principal stress on the anode increases as the steam-to-carbon ratio increases. Increasing the porosity reduces the length of the three-phase boundary, thereby decreasing the current density and the overall temperature and thermal stress on the anode. This study revealed the effects of operating conditions on the methanol-fueled SOFC, especially on the rib, and contribute to controlling the operant conditions for SOFC fueled by a mixture of steam and methanol. A three-dimensional model of a methanol-fueled solid oxide fuel cell is developed, considering the influence of rib. A high proportion of water in the fuel increases the thermal stress within the anode. The rib affects the distribution of the methanol decomposition reaction rate within the anode. By increasing the porosity of the anode, the thermal stress at the position under the rib can be reduced.