Nowadays, the usage of environment-friendly energy converter devices is getting more and more attention due to environmental crises and regulations. SOFCs are among the highly efficient chemical to electrical energy converters. Thus, their effectiveness is a significant issue to improve. To increase the efficiency of SOFCs, their properties should be investigated. However, it is costly and time-consuming to test all the essential characteristics of a solid oxide fuel cell by experimental methods. Computational methods can contribute to evaluating the influence of each parameter on the performance of the fuel cell. In this paper, a 3D mathematical model of a SOFC is presented. The model can describe the fuel cell’s temperature, material concentration and current distribution inside the cell. Also, the influence of the flow pattern (co-current and counter current) on the distribution plots and performance of the solid oxide fuel cell is investigated. The results demonstrate that the distribution of the current, concentration, and temperature is firmly related and wherever the concentration of reactants is higher, the temperature and current increase too. Also, the plots of power density and cell potential versus current were in consistence with the results of the literature. Moreover, comparison between two types of flow patterns shows that there is no significant variation when the type of current changes from counter to co-current. However, the performance of the SOFC is mildly better with a co-current flow pattern.