A mathematical model to simulate the diffusion phenomenon associated with change of volume in a rubbery polymeric membrane is developed. The model is based on a concentration-dependent diffusion coefficient. The continuity equation is integrated, by assuming that the thickness varies linearly with the mass absorbed. Solutions for small and large values of time are achieved. Then, these are matched to obtain the general solution, for the whole range of time. The resulting matching expression is valid for rigid solid and for those that suffer a great change of volume due to swelling. The results predicted by this equation are compared with experiments reported by different authors for these cases, finding very good coincidence. As will be shown the so-called sigmoidal behavior of the uptake curve can also be due to membrane shrinking.