Method for manufacturing a metal cord with three concentric layers including a first layer of diameter dc made up of M wire(s) of diameter d1, around which layer are wound together as a helix at a pitch p2, as a second layer, N wires of diameter d2, around which are wound as a helix at pitch p3, as a third layer, P wires of diameter d3. The N wires of the second layer are assembled around the layer to form, at a point called “assembling point”, an intermediate cord called “core strand” of M+N construction; upstream and/or downstream of the assembling point, the layer and/or the core strand is sheathed with a rubber or rubber composition by passing through at least one extrusion head; then the P wires of the third layer are assembled around the core strand to form a cord of M+N+P construction thus rubberized from the inside.