Structural stability issues in planar solid oxide fuel cells arise from the mismatch between the coefficients of thermal expansion of the components. The stress state at operating temperature is the superposition of several contributions, which differ depending on the component. First, the cells accumulate residual stresses due to the sintering phase during the manufacturing process. Further, the load applied during assembly of the stack to ensure electric contact and flatten the cells prevents a completely stress-free expansion of each component during the heat-up. Finally, thermal gradients cause additional stresses in operation. The temperature profile generated by a thermo-electrochemical model implemented in an equation-oriented process-modelling tool (gPROMS) was imported into finite-element software (ABAQUS) to calculate the distribution of stress and contact pressure on all components of a standard solid oxide fuel cell repeat unit. The different layers of the cell, i.e. anode, electrolyte, cathode and compensating layer were considered in the analysis by using the sub-modelling capabilities of the finite-element tool. Both steady-state and dynamic simulations were performed, with an emphasis on the cycling of the electrical load. The study includes two different types of cells, operation under both thermal partial oxidation and internal steam-methane reforming and two different initial thicknesses of the air and fuel compressive sealing gaskets. The results generated by the models are presented in two papers: Part I, focuses on the assessment of the risks of failure of the cell, which was performed by Weibull analysis, while the issues related to the other components are discussed in Part II. Only the anode support contributed to the probability of failure, since the other layers underwent compressive stresses independently of the operating conditions. The cell at room temperature after the reduction procedure was revealed as a critical case. Thermal gradients and the shape of the temperature profile generated during transient operation induced high probabilities of failure. The computed reliability is incompatible with commercialisation, but the scatter induced by the experimental data covers several orders of magnitude. Alternatively, the computed required strength of the anode material to fulfil a probability of failure of 10−2 in a 50-cells stack during steady-state operation appears achievable. Finally, extreme care is required when using the maximum thermal gradient or temperature difference over the SRU as an indicator for cell cracking.