The stress distribution and stress amplitude of a membrane are major factors to decide the mechanical fatigue life of PEMFC (Polymer Electrolyte Membrane Fuel Cell). In this paper, mechanical stresses under operating hygro-thermal condition of the membrane are numerically modelled. Contact analysis between gas diffusion layer (GDL) and the membrane is performed under various temperature-humidity conditions. The structural model has nonlinear material properties depending on temperature and relative humidity. Several geometric conditions are applied to the model. The numerical analysis results indicate that deformations of the membrane are strongly related with assembly conditions of the fuel cell. The fatigue life is predicted for practical operating condition through experimental data.