Thermal stresses and probability of failure of a functionally graded solid oxide fuel cell (SOFC) are investigated using graded finite elements. Two types of anode-supported SOFCs with different cathode materials are considered: NiO-YSZ/YSZ/LSM and NiO-YSZ/YSZ/GDC-LSCF. Thermal stresses are significantly reduced in a functionally graded SOFC as compared with a conventional layered SOFC when they are subject to spatially uniform and non-uniform temperature loads. Stress discontinuities are observed across the interfaces between the electrodes and the electrolyte for the layered SOFC due to material discontinuity. The total probability of failure is also computed using the Weibull analysis. For the regions of graded electrodes, we considered the gradation of mechanical properties (such as Young's modulus, the Poisson's ratio, the thermal expansion coefficient) and Weibull parameters (such as the characteristic strength and the Weibull modulus). A functionally graded SOFC showed the least probability of failure based on the continuum mechanics approach used herein. (C) 2010 Elsevier B.V. All rights reserved.