A comprehensive 3D mathematical model has been developed to study the performance of the planar anode-supported solid oxide fuel cell (SOFC) with different flow field designs such as helical, single-entry serpentine, traditional parallel, modified parallel design, double-entry serpentine and triple-entry serpentine. The model includes charge transport (electron and ion), conservation of mass, momentum, and energy. The developed model is numerically simulated and the predicted results are validated using the available experimental data from previous work. Results showed that single-entry cells suffer of back flow at the outlet of the cathode flow side in both helical and single-entry serpentine designs due to early full fuel consumption. To avoid back flow, increasing the number of entry ports at inlets and outlets in different designs is performed to increase the inlet mass flow rate. It is found that the triple-entry serpentine design attains good uniform distributions for both fuel and oxygen throughout the active surface area and achieves a high collected current of about 23.3 A with a percentage increase of 5.18% compared to the other designs at low voltage. Comparison with other designs indicates that the triple-entry serpentine gives better performance.