A method of manufacturing an elongate insert configured to be integrated by CIC in a metal container, including coated yarns bonded together, the coated yarns being formed from metal-coated ceramic fibers. The method includes placing the coated yarns side by side in a bundle and pulling the fiber bundle through a shaping element so as to compact the fiber bundle transversely while forming the fiber bundle so as to have a defined cross section. A metal part incorporating a fibrous insert can be manufactured by the CIC technique.