A process for producing tubular ceramic structures of non-circular cross section is provided which comprises: (a) rotating a mandrel-spindle assembly having a non-circular external cross section corresponding to the non-circular internal cross section of the tubular ceramic structure to be produced, the mandrel-spindle assembly comprising a mandrel component and a spindle component the mandrel component being a heat shrinkable polymeric tube of non-circular cross section the external surface of which corresponds to the internal surface of the tubular ceramic structure of non-circular cross section to be produced and the internal surface of which defines a bore the spindle component having a non-circular cross section corresponding to that of the bore of the mandrel and being in close fitting but slidably removable contact therewith; (b) applying a ceramic-forming composition to the external surface of the mandrel component of the rotating mandrel-spindle assembly to produce a tubular ceramic structure of non-circular cross section the internal surface of which is in contact with the external surface of the mandrel; (c) removing the spindle from the bore the mandrel to provide a mandrel-tubular ceramic structure assembly which the interior surface of the tubular ceramic structure of non-circular cross section remains in contact with the external surface of the mandrel and, (d) heat shrinking the mandrel component of the mandrel-tubular ceramic structure assemby to cause the mandrel to undergo shrinkage to a reduced size in which the external surface of the mandrel separates from the interior surface of the tubular ceramic structure of non-circular cross section facilitating removal of the mandrel therefrom. (a) rotating a mandrel-spindle assembly having a non-circular external cross section corresponding to the non-circular internal cross section of the tubular ceramic structure to be produced, the mandrel-spindle assembly comprising a mandrel component and a spindle component the mandrel component being a heat shrinkable polymeric tube of non-circular cross section the external surface of which corresponds to the internal surface of the tubular ceramic structure of non-circular cross section to be produced and the internal surface of which defines a bore the spindle component having a non-circular cross section corresponding to that of the bore of the mandrel and being in close fitting but slidably removable contact therewith; (b) applying a ceramic-forming composition to the external surface of the mandrel component of the rotating mandrel-spindle assembly to produce a tubular ceramic structure of non-circular cross section the internal surface of which is in contact with the external surface of the mandrel; (c) removing the spindle from the bore the mandrel to provide a mandrel-tubular ceramic structure assembly which the interior surface of the tubular ceramic structure of non-circular cross section remains in contact with the external surface of the mandrel and, (d) heat shrinking the mandrel component of the mandrel-tubular ceramic structure assemby to cause the mandrel to undergo shrinkage to a reduced size in which the external surface of the mandrel separates from the interior surface of the tubular ceramic structure of non-circular cross section facilitating removal of the mandrel therefrom.