A full three-dimensional, non-isothermal computational fluid dynamics model of a proton exchange membrane (PEM) fuel cell with straight flow field channels has been developed to simulate the hygro and thermal strains in a polymer membrane, which developed during the cell operation. This comprehensive model accounts for the major transport phenomena in a PEM fuel cell: convective and diffusive heat and mass transfer, electrode kinetics, transport and phase-change mechanism of water, and potential fields. The model is shown to understand the many interacting, complex electrochemical, transport phenomena, and stresses distribution that have limited experimental data. This model is used to study the effect of design parameters on the behavior of the polymer membrane. The results of this study helped us identify critical parameters and shed insight into the physical mechanisms leading to a fuel cell performance under various operating conditions. The results show that the nonuniform 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. These stresses in the membrane may explain the occurrence of cracks and pinholes in the membrane under steady-state loading during regular cell operation.