Experimental results from H2S solid oxide fuel cells (SOFCs) exhibit characteristics, e.g., an unusual dependence of cell performance on fuel composition and flow rate, which are poorly explained in current literature. In this paper, we demonstrate the importance of multiphysics modeling in understanding these results. We present a fully coupled two-dimensional multiphysics model that accounts for all transport processes and the chemical/electrochemical reactions in a working H2S SOFC including H2S dissociation kinetics in the fuel channels and heat transfer in the entire fuel cell assembly. A key aspect of the model developed in this work is the ability to model the coupled transport and reaction processes with thermodynamically consistent rate equations for the chemistry and electrochemistry. Simulation results from this comprehensive multiphysics model suggest that for the anode material used in our experiments, the electrochemically active species is H2S and not H-2. The model developed here allows the simulation of an SOFC with an anode that can electro-oxidize more than one fuel species, and we present results for the mixed open-circuit voltage from such a simulation.