Natural gas appears to be a fuel of great interest for SOFC systems. The principal component of natural gas is methane, which can be converted into hydrogen by direct or gradual internal reforming (DIR or GIR) within the SOFC anode. However, DIR requires a large amount of steam to produce hydrogen. If the injected mixture contains very small quantities of steam, GIR is then obtained. With GIR, the risk of carbon formation is even greater. This paper proposes a model and simulation, using the CFD-Ace software package, of the behaviour of a tubular SOFC using GIR and a comparison between utilization in DIR and GIR. A thermal study is included in the model and a detailed thermodynamic analysis is carried out to predict the carbon formation boundary for SOFCs fuelled by methane. Thermodynamic equilibrium calculations taking into account Boudouard and methane cracking reactions allowed us to investigate the occurrence of carbon formation. Simulations were used to calculate the distributions of partial pressures for all the gas species (CH4, H-2, CO, CO2, H2O), current densities and potentials in both electronic and ionic phases within the anode part (i.e., gas channel and cermet anode). The simulations indicate that there is no decrease in electrochemical performance if GIR is used rather than DIR. A thermal study appears to confirm that the cooling effect due to the endothermic reforming reaction is eliminated in GIR, but the thermodynamic study indicates that carbon formation can be suspected for x(H2O)/x(CH4) ratios lower than one. (c) 2006 Elsevier Ltd. All rights reserved.