Durability is one of the most critical remaining issues impeding successful commercialization of broad PEM fuel cell transportation energy applications. Automotive fuel cells are likely to operate with neat hydrogen under load-following or load-levelled modes and be expected to withstand variations in environmental conditions, particularly in the context of temperature and atmospheric composition. In addition, they are also required to survive over the course of their expected operational lifetimes i.e., around 5,500 hrs, while undergoing as many as 30,000 startup/shutdown cycles. The damage mechanisms in a PEM fuel cell are accelerated by mechanical stresses arising during fuel cell assembly (bolt assembling), and the stresses arise during fuel cell running, because it consists of the materials with different thermal expansion and swelling coefficients. Therefore, in order to acquire a complete understanding of the damage mechanisms in the membrane, mechanical response under steady-state hygro-thermal stresses should be studied under real cell operating conditions and in real cell geometry (three-dimensional). In this work, full three-dimensional, non-isothermal computational fluid dynamics model of a PEM fuel cell has been developed to simulate the stresses inside the PEM fuel cell, which are occurring during fuel cell assembly (bolt assembling), and the stresses arise during fuel cell running due to the changes of temperature and relative humidity. A unique feature of the present model is to incorporate the effect of hygro and thermal stresses into actual three-dimensional fuel cell model. In addition, the temperature and humidity dependent material properties are utilize in the simulation for the membrane. The model is shown to be able to understand the many interacting, complex electrochemical, transport phenomena, and stresses distribution that have limited experimental data. This model is used to study and analyse the effect of operating parameters on the mechanical behaviour of PEM. The analysis helped identifying critical parameters and shed insight into the physical mechanisms leading to a fuel cell durability for vehicular applications.