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 in exception of the cathode, i.e. anode, electrolyte and compensating layer were considered in the analysis to account for the cell curvature. 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 cell, 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 cell cracking. In the present paper, Part II, the occurrences of loss of gas-tightness in the compressive gaskets and/or electrical contact in the gas diffusion layer were identified. In addition, the dependence on temperature of both coefficients of thermal expansion and Young's modulus of the metallic interconnect (MIC) were implemented in the finite-element model to compute the plastic deformation, while the possibilities of thermal buckling were analysed in a dedicated and separate model. The value of the minimum stable thickness of the MIC is large, even though significantly affected by the operating conditions. This phenomenon prevents any unconsidered decrease of the thickness to reduce the thermal inertia of the stack. Thermal gradients and the shape of the temperature profile during operation induce significant decreases of the contact pressure on the gaskets near the fuel manifold, at the inlet or outlet, depending on the flow configuration. On the contrary, the electrical contact was ensured independently of the operating point and history, even though plastic strain developed in the gas diffusion layer.