Adequate mechanical compression applied to a proton exchange membrane fuel cell is essential for enhancing performance and durability. The compression not only improves the intimate contact between each layer component, but also causes significant deformation of the gas diffusion layer (GDL). As a result, the level of compression results in changes of electrical and thermal contact resistances, and anisotropic distribution of porosity and tortuosity in the GDL. To improve the fundamental understanding of the compression effect, a comprehensive two-phase model coupling solid mechanics, heat and mass transfer, and electrochemical reactions is developed. First, the model results are validated and show good agreement with the experimental data at baseline operating conditions of 80 degrees C, 200 kPa, 80% relative humidity, and 20% compression strain ratio with hydrogen and air. Then, oxygen, temperature and liquid saturation distribution at low, intermediate and high current densities are studied at the baseline compression level (20% strain). Finally, five compression strain ratios ranging from 5%, 10%, 15%, 20% and 25% are investigated to study the effect on stress distribution, transport properties, and fuel cell performance. Our results indicate that significant GDL deformation and channel intrusion are caused by land and rib distribution. As a combined effect from heat and mass transport, the liquid water condensation tends to initiate near the rib/GDL interface and can reach near 30% saturation at high current density. In addition, significant difference of in-plane temperature, oxygen, current, and load distributions can be observed due to the geometric aspect ratio and anisotropic GDL properties. A compression strain ratio of 20% is found to have an optimal performance balancing between high contact resistance caused by low compression and high transport resistance due to high compression. The findings of this study provide a new insight to the understanding the complicated coupling effect between mechanical, thermal, mass transport, and electrochemical multiphysics. (c) 2021 Elsevier Ltd. All rights reserved.