Over the last decade, many computational models have been presented to describe the complex thermomechanical behaviour of solid oxide fuel cells. The present study elucidates a detailed literature review of the proposed numerical models, ranging from a single channel or unit layer, up to coupled 3D high-end system models. Thermomechanical modelling foundations, including material properties and thermomechanical stress sources in SOFCs are emphasized. Employed material models for SOFC components are highlighted. Thermomechanical modelling issues such as geometrical idealisation, initial and boundary conditions for the highly coupled fluid and solid mechanics problem, as well as numerical solutions have been discussed. Thermomechanical stress-strain formulation of the common fuel cell components is highlighted. Finally, an overview of the numerically solved thermomechanical modelling studies in solid oxide fuel cells is given. Case studies are used throughout this review to exemplify and shed light on several modelling aspects. (C) 2014 Elsevier Ltd. All rights reserved.