A method of producing self-supporting ceramic composite bodies of desired shape by infiltrating a permeable self supporting preform with polycrystalline matrix material comprising an oxidation reaction product obtained by oxidation of a parent metal precursor, such as aluminum, and optionally containing therein metallic constituents. The composite body is formed by contacting a zone of a permeable self supporting preform, having at least one defined surface boundary spaced from said contacting zone, with a body of molten metal which is reacted with a suitable vapor-phase oxidant to form an oxidation reaction product. Within a certain temperature region, and optionally with one or more dopants in or on the parent metal or said permeable preform, molten parent metal migrates through previously formed oxidation reaction product into contact with the oxidant, causing the oxidation reaction product to grow into the preform toward said defined surface boundary so as to infiltrate the preform up to said defined surface boundary with the oxidation reaction product, and providing the composite structure of desired geometry.