An alumina fiber structure of a flat shape composed of alumina fibers having an alumina content of at least 65% by weight, the majority of said fibers being oriented substantially in parallel with the flat surfaces of the structure, and a number of fiber strands composed of the same alumina fibers extending inwardly from the flat surfaces of the structure, said structure having a thickness of from 4.8 mm to less than 10 mm, a density of from 0.07 to 0.3 g/cm.sup.3, a tensile strength of at least 0.5 kg/cm.sup.2 and a peeling strength of at least 0.5 kg/m.