Abstract A detailed numerical three-dimensional (3D) model for a planar solid oxide fuel cell (SOFC) is developed in this paper. The 3D model takes into account detailed processes including transport, chemical and electrochemical processes taking place in the cell. Moreover, effects of the composite electrodes are taken into account by considering an electrochemically active layer of finite thickness in each of the electrodes. The developed model is applied to a repeating unit of an anode-supported SOFC working under direct internal reforming conditions. Detailed results for chemical species, temperature, current density and electric potential distribution are presented and discussed. It was found that the temperature distribution across the cell is more uniform in the interconnects than in the inner part of the cell. However, only small differences in the electric potential between the electrode and the corresponding interconnect are found. The current density in the electrodes is found to be high near the electrolyte and low deep into the electrochemically active layer. The current density is also low under the ribs of the interconnects.