Direct Internal Reforming (DIR) on Solid Oxide Fuel Cell (SOFC) anodes is often considered for fuel cells systems utilising carbon based fuels. Methane Steam Reforming (MSR) is one of the most extensively studied types of DIR. The hydrogen formed by the MSR reaction can be electrochemically oxidised in the fuel cell to produce electricity, while the exothermic electrochemical reaction supplies heat to the endothermic MSR reaction. The balance is delicate and unsuitable design choices will result in operational problems and poor fuel cell performance. These issues are known for over two decades now and remain unsolved despite several attempts to capture the rate limiting kinetics of the reforming process on fuel cell anodes and modelling studies of methane fuelled SOFCs. It is not yet clear whether MSR kinetics derived from substrate measurements can be used to model SOFC performance and the influence of electrochemistry on the MSR reaction kinetics is rarely reported. In this work a rate equation is selected based on experimental observations and kinetics proposed in literature, on both industrial catalysts and SOFC anode materials. Ideal reactor models are derived for two specific test setup geometries, considering the electrochemical reactions in the anode. The ideal reactor models are then used to fit the parameters of the selected rate equation to experimental data from earlier work. The selected rate equation is of the Langmuir-Hinshelwood-Hougen-Watson type. The rate determining kinetics are characterised by the slow reaction of surface adsorbed carbon hydroxide forming carbon monoxide and atomic hydrogen. In addition surface coverage of atomic oxygen on the catalyst is limiting the available number of reaction sites. Two constants and their respective energies, associated with the activation of the rate limiting kinetics and the surface adsorption of oxygen, are fitted to experimental data. To evaluate the selected rate equation Computational Fluid Dynamics (CFD) type models are developed for the two experimental setups, one with a Ni?GDC anode and the other utilising a Ni?YSZ anode. These model are used to solve fluid dynamics, heat transfer, species transport, and electrochemistry. To model methane steam reforming in the fuel cell anode the selected rate equation is implemented in the CFD models. The obtained models are used to simulate MSR on the fuel cell anode for the experimental conditions. The modelled methane conversions and I-V characteristics are compared to the experimental values. The spatial distributions in the anode predicted with the selected rate equation and a power law model, fitted to the same experimental data, are compared to evaluate the use of global reaction models. For the Ni?GDC anode setup the model predicts the experimental methane conversions with good accuracy: the R2 value is with 0.987 close to unity. The experimental and modelled I-V characteristics are in good agreement. The model adopting a power law reaction mechanism underestimates the gradients in the anode. However, the model shows poor agreement with the experimental results obtained on the Ni?YSZ test setup. Large deviations with the temperatures and concentrations assumed in the ideal reactor model are found which might explain the inaccuracy of the model. The good agreement on the Ni?GDC anode suggests that MSR kinetics in SOFCs can be modelled for both open and closed circuit conditions with an appropriate intrinsic rate equation. This was not confirmed for the Ni?YSZ anode. Therefore further investigation with a combined experimental and modelling ap- proach, preferably on similar setups, is required.