Failure of membranes used in polymer electrolyte fuel cells is attributed to the in-situ chemical degradation of the membrane that is further exacerbated by the mechanical stresses generated due to hygro-thermal cycling during fuel cell operation. The chemical radical attack on the polymer chains within the membrane leads to gradual loss of the material and randomly distributed stress concentration sites are created. These sites are then subjected to repeated swelling and shrinkage of the membrane, eventually leading to the appearance of micro-cracks and/or pin-holes in the membrane. To simulate the lifetime of a fuel cell membrane in such an environment, it is therefore important to consider both these effects that occur simultaneously in the membrane. A stochastic modeling approach is presented in this work that takes into consideration the rates of chemical and mechanical degradation of the membrane incorporated into a two-dimensional membrane lattice network. While the rate of chemical degradation is based on the solution of reaction kinetics occurring in a fuel cell membrane, the mechanical degradation rate is evaluated using a stress-biased, thermally activated process. Depending upon any given chemical and mechanical load, and using appropriate physical properties of the membrane, the model can predict, within reasonable error, the time to crack initiation in the membrane based on a probabilistic non-homogeneous Poisson-type process. The membrane lifetime predictions are validated against test data acquired for membranes subjected to accelerated stress tests.