A mechanically undensified aromatic polyimide foam is made from an aromatic polyimide precursor solid residuum and has the following combination of properties: a density according to ASTM D-3574A of about 0.5 pounds/ft.sup.3 to about 20 pounds/ft.sup.3 ; a compression strength according to ASTM D-3574C of about 1.5 psi to about 1500 psi; and a limiting oxygen index according to ASTM D-2863 of about 35% oxygen to about 75% oxygen at atmospheric pressure. The aromatic polyimide foam has no appreciable solid inorganic contaminants which are residues of inorganic blowing agents. The aromatic polyimide which constitutes the aromatic polyimide foam has a glass transition temperature (Tg) by differential scanning calorimetry of about 235.degree. C. to about 400.degree. C.; and a thermal stability of 0 to about 1% weight loss at 204.degree. C. as determined by thermogravimetric analysis (TGA).The aromatic polyimide foam has utility as foam insulation and as structural foam, for example, for aeronautical, aerospace and maritime applications.