Display omitted •Innovative elastic foam-bed reactor for continuous gas–liquid reactions.•Mass transfer intensification with a low additional electric power.•Original routes for supported carbonic anhydrase.•An intensified process for CO2 capture. Open-cell polymer foams are memory shape materials with remarkable transport properties. We have designed an elastic foam-bed reactor based on these features to intensify gas–liquid mass transfer of CO2 through in situ foam compression/decompression cycles. The cycles are ensured by a crankshaft and only a low additional electric power (<50 Watts) is required under upflow co-current conditions in order to improve the mass transfer by one order to magnitude compared to fixed foam-bed reactor (i.e. without cycles). CO2 capture is improved thanks to carbonic anhydrase-supported foam (1.3 mg of enzyme per cm3 of foam) using a supramolecular hydrogel for continuous applications.