Tubular ceramic structures of non-circular cross section, e.g., anode components of tubular fuel cells of non-circular cross section, are manufactured by applying ceramic-forming composition to the external non-circular surface of the heat shrinkable polymeric tubular mandrel component of a rotating mandrel-spindle assembly, removing the spindle from said assembly after a predetermined thickness of tubular ceramic structure of non-circular cross section has been built up on the mandrel and thereafter heat shrinking the mandrel to cause the mandrel to separate from the tubular ceramic structure of non-circular cross section.