Open cell foams obtained by the simultaneous coreaction of condensed flavonoid tannins with an alkoxylated fatty amine and polymeric diphenylmethane isocyanate yielded highly flexible/elastic polyurethane foams. Copolymerized amine/isocyanate/tannin oligomers were identified by C-13 NMR and MALDI-TOF spectroscopy. In general, between 30% and 50% of natural tannins is added to the components used to obtain polymerisation of the polyurethane. The characteristic of these new, partially biosourced polyurethanes is that the tannin present slows down burning, some of them can be made flame self-extinguishing and if burning they neither flow nor asperge flaming material around, contrary to what occurs with normal polyurethanes. This limits the possibility of transmitting fire to other materials in the same environment. Cyclic compression tests were carried out showing that after 50 cycles foam recovery was in excess of 80%.