Gas diffusion layer (GDL) is one of the critical components in proton exchange membrane fuel cells (PEMFCs) and plays several important roles, such as structural support, reactants permeation, water removal, electrons, and heat conduction. The assembly pressure on bipolar plate is an important factor that affects the performance of PEMFC stack. Not enough assembly pressure leads to leakage of fuels and high contact resistance. Too much pressure, on the other hand, results in damage to the GDL, which increases the GDL Ohmic resistance and interfacial contact resistance, and in turn influences the reactant transport and water removal. The objective of the present study is to develop a numerical model to predict the onset of GDL failure and obtain the maximum assembly pressure on bipolar plate. Composite micromechanical model is applied to calculate the effective elastic properties of GDL; strength failure criterion is established to judge GDL damage with the stress distribution; finite element method model is developed to show the failure zone and the failure propagation in GDL combining the estimated elastic properties and strength failure criterion. Toray TGP-H-060 carbon paper is introduced as a numerical example and the numerical results show good agreements with experimental results. This numerical prediction model is beneficial to understand the basic mechanism of GDL failure and helpful to guide the assembling of PEMFC stack.