A method for manufacturing an article made of a composite material including a polymer matrix reinforced by a fibrous structure, the method including: placing the fibrous structure on a substrate; forming a molding surface, covering the structure with a mating mold; and compacting the structure by moving the surface of the mating mold toward the surface of the substrate. The substrate includes a cylindrical portion and a wall positioned radially relative to the cylindrical portion, and the mating mold includes two portions that are mobile relative to one another and that are moved toward the axis of the cylindrical portion and towards the radial wall of the substrate, respectively. The method can be used for example for manufacturing a fan casing of a turbojet engine.