Open-cell structures are filled with polyimide foam formed in place by the use of a foam precursor in powdered form comprised of a combination of (a) the reaction product of an excess of organic polyisocyanate and a member selected from the group consisting of furfuryl alcohol and condensation products thereof, and (b) an organic polycarboxylic compound containing two carboxylic anhydride groups. The precursor is prepared by combining the species under conditions which favor the reaction of the furfuryl alcohol with the polyisocyanate, but not the polyimide-forming reaction. The polyimide-forming reaction itself is then performed by adding preselected amounts of the powdered precursor, depending on the desired ultimate density of the foam, to each cell of the open-cell structure, then heating to initiate the polyimide reaction, and permitting the carbon dioxide generated by the reaction to escape while confining the resulting foam to the cells.