A fully three-dimensional mathematical model of a planar solid oxide fuel cell (SOFC) with complete direct internal steam reforming was constructed to investigate the chemical and electrochemical characteristics of the porous-electrode-supported (PES)-SOFC developed by the Central Research Institute of Electric Power Industry of Japan. The effective kinetic models developed over the Ni/YSZ anode takes into account the heat transfer and species diffusion limitations in this porous anode. The models were used to simulate the methane steam reforming processes at the co- and counter-flow patterns. The results show that the flow patterns of gas and air have certain effects on cell performance. The cell at the counter-flow has a higher output voltage and output power density at the same operating conditions. At the counter-flow, however, a high hotspot temperature is observed in the anode with a non-fixed position, even when the air inlet flow rate is increased. This is disadvantageous to the cell. Both cell voltage and power density decrease with increased air flow rate.