Abstract: Internal reformation of low steam methane fuel is important for the high e ciency and low cost operation of solid oxide fuel cell. Understanding and overcoming carbon deposition is crucial for the technology development. Here a multi-physics model is established for the relevant experimental cells. Balance of electrochemical potentials for the electrochemical reactions, generic rate expression for the methane steam reforming, dusty gas model in a form of Fick's model for anode gas transport are used in the model. Excellent agreement between the theoretical and experimental current-voltage relations is obtained, demonstrating the validity of the proposed theoretical model. The steam reaction order in low steam methane reforming reaction is found to be 1. Detailed information about the distributions of physical quantities is obtained by the numerical simulation. Carbon deposition is analyzed in detail and the mechanism for the coking inhibition by operating current is illustrated clearly. Two expressions of carbon activity are analyzed and found to be correct qualitatively, but not quantitatively. The role of anode diffusion layer on reducing the current threshold for carbon removal is also explained. It is noted that the current threshold reduction may be explained quantitatively with the carbon activity models that are only qualitatively correct.