The development of fuel cells has progressed to portable applications recently. This paper conducts a Monte Carlo simulation (MCS) of a spatially-smoothed non-isothermal model to correlate the performance of a 3D 5-cell planar solid oxide fuel cell (P-SOFC) stack with the variability of modeling parameters regarding material and geometrical properties and operating conditions. The computationally cost-efficient P-SOFC model for the MCS captures the leading-order transport phenomena and electrochemical mechanics of the 3D stack. Sensitivity analysis is carried out in two scenarios: first, by varying modeling parameters individually, and second by varying them simultaneously. The stochastic parameters are ranked according to the strength of their correlations with global and local stack performances. As a result, different rankings are obtained for the two scenarios. Moreover, in the second scenario, the rankings change with the nominal values and variability of the stochastic parameters as well as local positions within the stack, because of compensating or reinforcing effects between the varying parameters. Apart from the P-SOFCs, the present MCS can be extended to other types of fuel cells equipped with parallel flow channels. The fast stack model allows statistical modeling of a large stack of hundreds of cells for high-power applications without a prohibitive computational cost. (C) 2014 Elsevier Ltd. All rights reserved.