The mechanical degradation of the proton exchange membrane (PEM) is one of the main aspects affecting the lifetime of proton exchange membrane fuel cells (PEMFCs). It was observed in our previous study that the stress/strain distribution in the PEM of fuel cells with metallic bipolar plates (BPPs) is more complex, owing to manufacturing and assembly errors of the BPPs. The present study further concentrates on the stress/strain evolution in the membrane of fuel cells throughout the assembly and running processes by a finite element model. In membranes at the joint area between the gasket and gas diffusion layers, a serious stress concentration aggravated as the misalignment displacement increases. As for the membrane in reaction area, the plastic strain reaches highest level at the center of the groove after hygrothermal loading. The maximum stress is mainly relevant to the temperature and humidity and has little concern with the misalignment. The model and results of this study offer guidance regarding the design of PEMFC. Owing to the stress concentration, an additional protection should be set in the joint area, and the assembly error should be limited within 0.05 mm.