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The solid oxide fuel cell (SOFC) is a direct energy conversion device, which allows the production of electricity with high efficiency while maintaining pollutant emissions at a low level. It offers better fuel flexibility and lower vulnerability to impurities in the oxidising and fuel gases than other fuel cells. The lack of reliability and durability of SOFC devices currently impedes their large-scale commercialisation. The mitigation of mechanical and electrochemical degradation that together limit the lifetime, requires the precise understanding of the phenomena. The underlying processes act and interact at different spatial and temporal scales, which complicates characterisation and, consequently, the identification of the dominant contributions to the observed overall degradation in field conditions. This thesis has developed a modelling framework to investigate electrochemical and mechanical reliability and durability issues in planar, intermediate-temperature SOFC stacks based on anode-supported cells. The approach consisted in coupling thermo-electrochemical and thermo-mechanical continuum models, spanning from the electrode micro-scale to the stack macro-scale, to include in the analysis the detrimental interactions between the different phenomena that provoke failure after combined prolonged operation and cycling conditions. To achieve this aim, the existing cleavages between the research fields had to be bridged. At each sub-scale and for each aspect of interest, data was first gathered to identify the needed and achievable level of complexity of the description, and to calibrate the models using parameter estimation. Then, specific studies to understand the key dependences on the local conditions and limitations of the proposed approaches were carried out. Finally, the sub-models were implemented together in SRU/stack models to capture the multi-factorial and progressive nature of immediate or delayed failures in SOFCs. The implementation of a calibrated electrochemical model with degradation phenomena in SOFC stack models shed light on the micro- and macro-scale interactions that cause the progressive activation of the electrochemical degradation phenomena. Dynamic optimisation identified the critical decision variables, in terms of operating conditions, whereas disparities in the electrochemical and mechanical properties of the materials, stack design and constraints from the system were further included, to propose case-specific mitigation procedures. The results ascertained the predominant effect of overpotential, rather than current density, on the electrochemical degradation, as it governs the chromium contamination and the formation of undesirable insulating phases in the cathode. In the most striking cases, the lifetime could be extended by a factor of up to five, by the sole adjustments of the operating conditions. Counter-flow configuration, with low methane conversion in the reformer, is more favourable than co-flow. The thermo-mechanical contact model enlarged the analysis with insights into the complex failure modes, which ultimately cause the mechanical failure of the cell directly or indirectly, through a succession of deleterious events. The model explains the difficulty to ensure the integrity of the cells, the electrical contact and gas-tightness of the compartments, while preventing thermal buckling, during load following and thermal cycling. The effects of design and history were analysed in light of thermo-electrochemical and mechanical degradation, combined with rate-independent plasticity and creep, and stacking conditions. For the first time, to our knowledge, the modelling framework developed here has encompassed both electrochemical and mechanical degradation, along with calibration procedures, for lifetime predictions and identification of complex failure modes. This capability is expected to contribute significantly to improve the durability of SOFC devices in the future, since most of the modelled issues are currently addressed by progressive empirical adjustments.