Reversible solid oxide fuel cells (rSOFCs) may be applied to store and generate electrical energy in a reversible mode. This technique is promising to balance the conflict between intermittent power supply and demand in a sustainable way. One of the limitations of the development of rSOFCs is the high cost of storage and usage of pure H-2, which may be solved by employing syngas as the fuel. The performance of rSOFCs depends on the development of bifunctional materials, cell design, and operation optimization, which are often investigated and predicted by the cost-effective approach of mathematical modeling. However, the modeling of dual-mode rSOFCs involving co-redox reactions with syngas is not well developed. In this study, a two-dimensional (2D) single-channel model of an rSOFC is developed. The novelty of this model is that the multiphysics transport processes are fully coupled and solved with the reversible water-gas shift reaction with syngas and the electrochemical reactions. The effects of the operating conditions and design parameters (eg, electrode thickness) are considered, with the aim of providing guidelines to optimize the design and operation of reversible cells. It is concluded that the thickness of the electrode has a larger impact on the water-gas shift reaction than on the electrochemical reaction in both the gas diffusion and reaction regions. The C/H element ratio of syngas has a negative correlation with power output, but the distributions of current and gas species may be improved in both modes. A higher operating temperature improves the performance in both modes but has a more substantial effect in the electrolysis mode. The specific design and operating schemes favored in different modes should be balanced in the reversible mode.