A three-dimensional, multi-phase, non-isothermal computational fluid dynamics model of a proton exchange membrane fuel cell has been developed and used to investigate the displacement, deformation, and stresses inside the whole cell, which developed during the cell operation due to the changes of temperature and relative humidity. The behaviour of the fuel cell during operation has been studied and investigated under real cell operating conditions. A unique feature of the present model is to incorporate the effect of hygro and thermal stresses into actual three-dimensional fuel cell model for a complete cell with both the membrane-electrode-assembly and the gas distribution flow channels. The results show that the non-uniform distribution of stresses, caused by the temperature gradient in the cell, induces localized bending stresses, which can contribute to delaminating between the membrane and the gas diffusion layers. The non-uniform distribution of stresses can also contribute to delaminating between the gas diffusion layers and the channels, especially in the cathode side. These stresses may explain the occurrence of cracks and pinholes in the fuel cells components under steady-state loading during regular cell operation, especially in the high loading conditions.