When moisture uptake in a polymer is associated with swelling, it induces stresses which interact with the entire diffusion process. This coupling is addressed in this paper, which extends immediately to the diffusion of other fluids, like solvents. First, the generalized chemical potential is used to analyze the effect of stresses on the moisture capacity of polymers, and a relation is derived as a function of material parameters. Then, the interactions between stress and diffusion before saturation is reached, are explored. Various effects are predicted on the classical sorption test, such as an evolution of the boundary condition with time, and a sorptiondesorption hysteresis.