Abstract: A method of manufacturing an axisymmetric component made of a composite material having a metallic matrix is described in which at least one ceramic fiber and at least one wire of the metal which is to constitute the matrix are wound simultaneously side by side to form a number of layers on a suitably shaped mandrel and in such a manner as to ensure absence of contact between the fiber turns of each individual layer and between the fiber turns of adjacent layers, and the formed layers are subsequently subjected to hot isostatic compaction. The ceramic fiber may be of the silicon carbide type and the metal wire forming the matrix may be of titanium or titanium-alloy.