We study a semi-discrete nite element approximation of weak solutions to a moving boundary problem that models the di usion of solvent into rubber. We report on both a priori and a posteriori error estimates for the mass concentration of the di usants, and respectively, for the position of the moving boundary. Our working techniques include integral and energy-based estimates for a nonlinear parabolic problem posed in a transformed xed domain combined with a suitable use of the interpolation-trace inequality to handle the interface terms. Numerical illustrations of our FEM approximations are within the experimental range and show good agreement with our theoretical investigation. This is joint work with Y. Wondmagegne and A. Muntean (Karlstad, Sweden)