Multistrand metal cord consisting of K elementary strands assembled in a helix, each elementary strand: o consisting of a cord having two layers (Ci, Ce) of L+M construction, rubberized in situ, comprising an inner layer (Ci) consisting of L wires of diameter d 1, L varying from 1 to 4, and an outer layer (Ce) of M wires, M being equal to or greater than 5, of diameter d 2, which are assembled in a helix with a pitch p 2 around the inner layer (Ci); its inner layer (Ci) is sheathed with a rubber composition called a "filling rubber"; each elementary strand having the following characteristics (d 1, d 2 being expressed in mm): - 0.10 <d 1 < 0.50; - 0.10 < d 2 < 0.50; characterized in that each elementary strand has the following characteristics (p 2 being expressed in mm): - 3 < p 2 < 10; - said K elementary strand being assembled in a helix with a helix pitch P K, over any length of the elementary strand equal to K times P K, the filling rubber is present in each of the capillaries delimited by the L wires of the inner layer (Ci) and the M wires of the outer layer (Ce), and also, when L is equal to 3 or 4, in the central channel delimited by the L wires of the inner layer (Ci); and - the amount of filling rubber in said elementary strand is between 5 and 40 mg per g of elementary strand; - each elementary strand has no filling rubber on its periphery; and in that the cord is a one layer cord and of the Kx(L+M) construction. o consisting of a cord having two layers (Ci, Ce) of L+M construction, rubberized in situ, comprising an inner layer (Ci) consisting of L wires of diameter d 1, L varying from 1 to 4, and an outer layer (Ce) of M wires, M being equal to or greater than 5, of diameter d 2, which are assembled in a helix with a pitch p 2 around the inner layer (Ci); its inner layer (Ci) is sheathed with a rubber composition called a "filling rubber"; each elementary strand having the following characteristics (d 1, d 2 being expressed in mm): - 0.10 <d 1 < 0.50; - 0.10 < d 2 < 0.50; characterized in that each elementary strand has the following characteristics (p 2 being expressed in mm): - 3 < p 2 < 10; - said K elementary strand being assembled in a helix with a helix pitch P K, over any length of the elementary strand equal to K times P K, the filling rubber is present in each of the capillaries delimited by the L wires of the inner layer (Ci) and the M wires of the outer layer (Ce), and also, when L is equal to 3 or 4, in the central channel delimited by the L wires of the inner layer (Ci); and - the amount of filling rubber in said elementary strand is between 5 and 40 mg per g of elementary strand; - each elementary strand has no filling rubber on its periphery; and in that the cord is a one layer cord and of the Kx(L+M) construction. - 0.10 <d 1 < 0.50; - 0.10 < d 2 < 0.50; - 3 < p 2 < 10; - said K elementary strand being assembled in a helix with a helix pitch P K, over any length of the elementary strand equal to K times P K, the filling rubber is present in each of the capillaries delimited by the L wires of the inner layer (Ci) and the M wires of the outer layer (Ce), and also, when L is equal to 3 or 4, in the central channel delimited by the L wires of the inner layer (Ci); and - the amount of filling rubber in said elementary strand is between 5 and 40 mg per g of elementary strand; - each elementary strand has no filling rubber on its periphery; and in that the cord is a one layer cord and of the Kx(L+M) construction.