The authors have been engaged in numerical simulations of the planar type solid oxide fuel cell (SOFC) to make clear the dependence of the cell performance on its operating conditions. Up to now, the authors have already developed the simulation codes for the one channel region and the single cell plate in its cell stack. To calculate accurately the effect of radiation heat transfer from the cell stack surfaces, however, a code that can treat the whole cell stack is necessary. In the present study, therefore, the authors newly develop a three dimensional simulator. code of the planar SOFC stack, and the detailed effect of the radiation heat transfer is investigated. It is made clear that the conventional codes are sufficiently accurate, and the newly developed whole cell stack code is not inevitable to predict the maximum cell temperature. This is because the thermal conductivity of the cell materials made of ceramics is very small, and the central part of the cell stack is almost free from the influence of radiation heat transfer. On the other hand, the stack simulation is needed to calculate accurately the cell voltage because the radiation heat transfer reduces it when the ambient temperature is low. The bad influence of low ambient temperature on the voltage is, however, small and relatively high voltage is obtained even when the ambient temperature is very low. (C) 2006 Elsevier Inc. All rights reserved.