The mechanical loads that gas diffusion layers (GDLs) withstand in polymer electrolyte membrane fuel cell (PEMFC) stacks are sensitive to the assembly and working conditions. The mechanical properties of GDLs mostly depend on their composition materials, microstructural characteristics, operation conditions, etc. An accurate and comprehensive understanding of the mechanical performance of GDLs is significant for predicting the stress distribution and improving the assembly technology of PEMFC stacks. This study presented a novel 3-D nonlinear and orthotropic constitutive model of a carbon paper GDL to represent the material stiffness matrix with its compressive, tensile, and shear properties. Numerical simulations were performed based on the 3-D constitutive model, and the proposed 3-D model was validated against the experimental data reported previously. It is found that the simulation results of the 3-D constitutive model show a good agreement with the experimental results. Besides, the novel 3-D nonlinear and orthotropic model was applied in the overall stress simulation of a simplified PEMFC unit cell, compared to a conventional 3-D linear and isotropic model, and the simulation results of the two models show a significant difference.