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Air plasma sprayed thermal barrier coating (APS TBC) systems are usually applied to engine components to reduce the temperature of the substrate and increase the efficiency of engines. However, failure of these coatings leads to oxidation and corrosion of the substrate. Therefore, a thorough understanding of the coating failure is necessary to predict the lifetime of coated components. This project has carried out stress analysis and prediction of subsequent failure of APS TBC systems associated with sintering of the TBC, oxidation of the bond coat (BC), substrate geometry, undulations at the coating interfaces and coating fracture toughness. Stress analysis is crucial for predicting TBC failure as stresses in the vicinity of the coating interfaces cause cracks and subsequent coating delamination. The Finite element (FE) method was used for stress analysis of TBC systems at high temperature stage and at cooling stage after operation. Initially, FE model of an axisymmetric unit cell representing the slice of a coated cylinder was used. Different radii for cylinders were used to investigate the significance of substrate curvature on coating stresses. The effect of asperities at the coating interface on residual stresses was observed using 3D models. The models were built based on the actual geometries of asperities, which were extracted from 3D SEM images of the coating interfaces. An Arrhenius approach was utilised to implement changes in mechanical and physical properties of TBC due to sintering. BC oxidation and related changes in its composition were also implemented. The accuracy of assumptions for FE models was validated by comparing the evaluated stresses against experimental results by project partners. Finally, the effects of stresses and fracture toughness of the coatings and coating interfaces on failure of the TBC system were studied, using cohesive surface modelling and extended finite element modelling (XFEM) methods.