PURPOSE: To obtain microtubular ceramic materials of self-supporting porous construction useful for a heat insulator or the like by bringing a specific metal catalyst into contact with gaseous hydrocarbon at a specific temperature, followed by the deposition of a conformable coating and by oxidation.

CONSTITUTION: The objective materials are obtained by bringing a metal catalyst for the growth of multidirectional carbon fiber into contact with at least one kind of gaseous hydrocarbons at a temperature sufficient to form carbon fiber and not sufficient for the pyrolytic deposition of carbon in a forming mold, followed by the deposition of a conformable coating made of a ceramic or ceramic-formable substance on the carbon fiber and then by heating the coated fiber in an oxygen-containing atmosphere for an enough time to vaporize (substantially) all carbon through oxidation. The conformable coating is preferably deposited by chemical vapor deposition or the like.