A structural model has been developed for analysis of residual stresses for anode- and electrolyte-supported planar solid oxide fuel cells (SOFC). This model was also used for analysis of thermally induced stresses during operation for three different case studies with the electrolyte-supported geometry. Temperature distribution in the solid parts of the cell was modeled by means of an in-house electrochemical model, and the results were exported to the structural model. In the case studies, the impact of air and fuel inlet temperatures, steam reforming, and operation voltages on thermal stresses were studied. Weibull statistics were used for the prediction of failure probabilities and design considerations. Base case geometry for the electrolyte-supported cell was 50, 150, and 50 μm for anode, electrolyte, and cathode thicknesses, respectively, and for the anode-supported cell 1000, 20, and 50 μm, respectively. Analysis of residual stresses showed that, compared with the anode-supported cell, the electrolyte-supported cell experienced considerably higher stress levels in the anode and cathode due to the thick electrolyte, while the stress levels in the electrolyte were lower. For the anode-supported cell, maximum stress levels were 57, −12, and −678 MPa in the anode, cathode, and electrolyte, respectively, with negative values indicating compressive and positive values, tensile stresses. For the electrolyte-supported geometry, the corresponding levels were 282, 100, and −308 MPa, respectively. With a failure probability of 1E-6 and an electrolyte thickness of 10 μm, the minimum allowable anode thickness was estimated to be 1000 μm. For an electrolyte-supported cell, optimal thicknesses of electrolyte and anode were considered to be 100 and 100 μm, respectively, while the thickness of the cathode showed low impact. During operation, the stress levels were reduced considerably, since high operating temperatures reduce the temperature difference to the sintering temperature (1250 °C). Concerning the presence of methane in the fuel and the effect of steam reforming, small amounts of methane—as low as 10% of molar mass—were found to induce a cooling effect with correspondingly high gradients. With 45% methane in the fuel, the tensile stress level in the anode was about 130 MPa; the impact of thermal gradients was considered to be 40 MPa and the cooling effect also 40 MPa.