One of the major barriers for polymer electrolyte membrane (PEM) fuel cells to be commercially viable for stationary and transportation applications is the durability of membranes undergoing chemical and mechanical degradation over the period of operation. Toward understanding the effects of operating parameters on membrane durability, this paper presents numerical simulations for a single channel PEM fuel cell undergoing changes in load, by subjecting a unit cell to step changes in voltage. The objective is to elucidate the mechanical response of the membrane, which is subjected to hygral (water) loading and unloading cycles at constant temperature. Detailed three-dimensional (3D) computational fluid dynamics (CFD) simulations are conducted, taking into account the complex interactions of water transport dynamics and load changes, to accurately capture the water content in the membrane with changes in cell voltage. The water content obtained through CFD simulations is, in turn, used to carry out two-dimensional (2D) finite element (FE) analysis to predict the mechanical response of the membrane undergoing cyclic change in water content, as the operating voltage is cycled. The effects of cyclic changes in cell potential on the stresses induced, amount of plastic strain, and its localization are analyzed for various inlet cathode humidity values for two sections along the length of the fuel cell.