The present invention relates to a three-layered metal cable of construction L+M+N usable as a reinforcing element for a tire carcass reinforcement, comprising an inner layer C1 having L wires of diameter d1 with L being from 1 to 4, surrounded by an intermediate layer C2 of M wires of diameter d2 wound together in a helix at a pitch p2 with M being from 3 to 12, said layer C2 being surrounded by an outer layer C3 of N wires of diameter d3 wound together in a helix at a pitch p3 with N being from 8 to 20, said cable being characterized in that a sheath formed of a cross-linkable or cross-linked rubber composition based on at least one diene elastomer covers at least said layer C2. The invention furthermore relates to the articles or semi-finished products made of plastics material and/or rubber which are reinforced by such a multi-layer cable, in particular to tires used in industrial vehicles, more particularly heavy-vehicle tires and their carcass reinforcement plies.