Proton exchange membranes (PEMs) in operating fuel cells are subjected to varying thermal and hygral loads while under mechanical constraint imposed within the compressed stack. Swelling during hygrothermal cycles can result in residual in-plane tensile stresses in the membrane and lead to mechanical degradation or failure through thinning or pinhole development. Numerical models can predict the stresses resulting from applied loads based on material characteristics, thus aiding in the development of more durable membrane materials. In this work, a nonlinear viscoelastic stress model based on the Schapery constitutive formulation is used with a viscoplastic term to describe the response of a novel membrane material comprised of a blend of perfluorocyclobutane (PFCB) ionomer and poly(vinylidene fluoride) (PVDF). Uniaxial creep and recovery experiments characterize the time-dependent linear viscoelastic compliance and the fitting parameters for the nonlinear viscoelastic viscoplastic model. The stress model is implemented in a commercial finite element code, abaqus®, to predict the response of a membrane subjected to mechanical loads. The stress model is validated by comparing model predictions to the experimental responses of membranes subjected to multiple-step creep, stress relaxation, and force ramp loads in uniaxial tension.