Metal cord (C-1) with two concentric layers (Ci, Ce) of M+N construction, comprising an internal first layer or core (Ci) made up of M wire(s) (10) of diameter d1, M varying from 1 to 4, around which core are wound together in a helix, in an external second layer (Ce), N wires (11) of diameter d2, in which at least some of the gaps in the cord which are situated between the wires of the various contain a filling rubber (13) based on an unsaturated thermoplastic elastomer, particularly a styrene thermoplastic elastomer (TPS) such an SBS or SIS block copolymer for example.Such a thermoplastic elastomer, when used in the molten state, presents no problems of unwanted stickiness if the filling rubber overspills outside the cord after manufacture; its unsaturated and therefore (co)vulcanizable nature makes it extremely compatible with the diene rubber, for example natural rubber, matrices usually used as calendering rubber in the metal fabrics intended for reinforcing the tyres.