This study deals with a multi parameter estimation problem with bounded output errors. It concerns the swelling of polymer films by a solvent, in the glassy state. Local thermodynamic equilibrium is no more ensured and the swelling results of two coupled phenomena, the diffusion of solvent on one hand and the change in solubility due to stress relaxation of the entangled polymer chains on the other hand. The estimation aims to obtain the parameters that characterise these two phenomena from gravimetric experiments. A set inversion analysis is used to perform the estimation: this global estimation method allows to determine all the sets of parameters that give a mass uptake consistent with the experimental data and the bounded errors. It gives interesting information on the coupling between the parameters and is well appropriate to analyse this ill-conditioned problem. A systematic analysis of the estimation performance as a function of the characteristics of the polymer/solvent system and of the experimental set-up have been performed.