Flexible nanoporous chromium or iron terephtalates (BDC) MIL-53(Cr, Fe) or M(OH)[BDC] have been used as matrices for the adsorption and in vitro drug delivery of lbuprofen (or alpha-p-isobutylphenylpropionic acid). Both MIL-53(Cr) and MIL-53(Fe) solids adsorb around 20 wt% of lbuprofen (lbuprofen/dehydrated MIL-53 molar ratio = 0.22(1)), indicating that the amount of inserted drug does not depend on the metal (Cr, Fe) constitutive of the hybrid framework. Structural and spectroscopic characterizations are provided for the solid filled with lbuprofen. In each case, the very slow and complete delivery of lbuprofen was achieved under physiological conditions after 3 weeks with a predictable zero-order kinetics, which highlights the unique properties of flexible hybrid solids for adapting their pore opening to optimize the drug-matrix interactions.