The solid-state ceramic construction of SOFCs enables high fuel to electricity conversion efficiencies of as high as 50 to 60 percent LHV in high temperature operation, and allows more flexibility in fuel choice. In this study, we have developed a symbolic analysis method to investigate the availability of variable parameters appearing in multi-stage electrochemical oxidation mechanism that is expected to further improve the electric efficiencies of SOFCs. In the flow system of the multi-stage oxidation, the fuel utilization, Uf, at the most downstream stack, UfM, is expressed as a function of number of stacks, n, and total fuel utilization, UfT. When n = 10 and UfT = 85%, UfM is calculated to be 36%, which is much smaller than UfT. Therefore, if the most downstream stack has high robustness against lean fuel gas, UfT could be set to higher values without serious degradation by using this flow system.