A 3-D finite element analysis (FEA) model of a 3-cell stack based on a prototype planar SOFC stack design was constructed to perform thermal stress analyses at shutdown and steady operation conditions. The constructed 3-D FEA model consists of complete planar SOFC components such as positive electrode-electrolyte-negative electrode (PEN) assembly, interconnect, nickel mesh, and gas-tight glass-ceramic seal. The thermal stress distributions at shutdown and steady-state stages as well as their dependence on the initial stress-free temperature and operation cycles were systematically evaluated. Modeling results indicated that the glass-ceramic sealant was the most critical part needed to be watched in terms of structural integrity, in particular at operation temperature where shear fracture of such a component was predicted. Localized plastic deformation was predicted for the metallic interconnect and frame at both shutdown and steady-state conditions. An increase in the initial stress-free temperature would significantly increase the thermal stresses in all of the components at both shutdown and steady-state stages. In addition, a notable increase of thermal stress with increasing cycle number in the PEN at steady-state stage as well as in the glass-ceramic sealant at shutdown stage was predicted.