Structural reliability is a hurdle for the large-scale commercialisation of solid oxide fuel cell (SOFC). The cells are prone to cracking, due to the brittleness of their constitutive materials. In operation, the failure of one of them can arise from the non-uniform temperature distribution, coupled to detrimental interaction with the other stack components. In the long-term, the uneven distribution of temperature, gas composition, current density or overpotential induces non-uniform creep deformation and microstructural alterations of the bulk or interfaces that can affect their strength. Therefore, the resistance of a stack towards thermal cycles and load following is expected to decrease with respect to operating time. Besides material improvements, proper stack design and control strategy are paramount to alleviate these detrimental phenomena. Owing to the multiphysics nature of the problem, this achievement requires modelling. The aim of the present paper is to provide the current state of existing models for the prediction of mechanical failures in SOFC stacks. In a first part, a brief overview on the mechanical behaviour of the cell, sealing and gas diffusion layer (GDL) materials is provided, along with a discussion on their implementation in finite-element (FE) software. The need for refined constitutive laws for plasticity and creep, as well as temperature and aging dependences is highlighted. Second, the outcome of simple models, such as derived from the beam theory, is presented. These enable preliminary investigations on the phenomena occurring in the cell during the sintering, the reduction/reoxidation of the anode or combined aging and thermal cycles. In the second part, the current modelling capabilities are illustrated with studies available in literature. A comprehensive analysis requires coupling a thermo-electrochemical model with a FE tool. At present, the temperature and/or vacancy profiles are exchanged. The choice of technological solutions, namely sealing/GDL system and cell type, defines the mechanical interaction between the components. One of our study cases, a planar design with anode-supported cells, is used to discuss the particularities of SOFC modelling: (i) initialisation steps, i.e. cell sintering, assembly, anode reduction and sealing procedures, (ii) boundary conditions representative of stacking of the repeating units and (iii) choice of suitable discretisation elements among those available in commercial FE tools. Existing models can potentially predict many of the structural issues observed in SOFC stacks, during discrete events, before or after aging, such as cracking of the cell or glass sealing, loss of contact pressure on GDLs or compressive gaskets and thermal buckling. However, the reliability of the predictions currently suffers from the lack of dedicated experimental validations.