An inorganic, phosphate-containing cellular material is manufactured from Portland cement, polyphosphoric acid and an expanding agent acting in an acidic medium. There may be added furthermore aluminous cement, oxides of calcium, zinc, aluminum, iron, hydroxides of aluminum and iron, fillers and reinforcing agents. By intense intermixing of the starting products a mixture is prepared which has an equivalent ratio of (Al+Mg+CA+Fe) to phosphate of 0.8:1 to 3.0:1. The mixture foams, is charged to a mold, heated if necessary to a temperature of 80.degree. C., and after completed exothermal reaction hardened under heat.