Rubber composition based on at least: - a copolymer A based on at least one ethylene monomer and on at least one vinyl acetate monomer; - a reinforcing inorganic filler comprising silica; - as agent for coupling between said copolymer A and said reinforcing inorganic filler, an organosilane compound of formula B-Z-Si(G 1) (3-d) (G 2) (d) in which: • B represents a functional group interacting with the copolymer A, the group B being chosen from vinyl groups, halogen atoms, unsaturated α,β-enones, acryloxy groups, methacryloxy groups, acrylamido groups, methacrylamido groups and amino groups, • Z represents a spacer group formed of a divalent hydrocarbon-based chain comprising from 1 to 18 carbon atoms and making it possible to connect the group B to the silicon atom; • G 1, which are identical or different, each represent a monovalent hydrocarbon-based group chosen from linear or branched alkyls having from 1 to 18 carbon atoms, substituted or unsubstituted cycloalkyls or aryls having from 5 to 18 carbon atoms, substituted or unsubstituted alkenyloxyls having from 2 to 18 carbon atoms, substituted or unsubstituted aryloxy or aralkyloxy groups having from 6 to 18 carbon atoms, or a monovalent group in the form R 1 -(-O-(CJ 2) a) b -O- in which J represents a hydrogen, a phenyl group or an alkyl group having from 1 to 4 carbon atoms, b is an integer within the range 1 to 18 and a is an integer within the range 1 to 6, and R 1 being chosen from linear or branched, substituted or unsubstituted alkyls having from 1 to 4 carbon atoms or linear or branched, substituted or unsubstituted alkoxyls having from 1 to 4 carbon atoms, • G 2, which are identical or different, each represent a monovalent group chosen from the hydroxyl (-OH) group, linear or branched, substituted or unsubstituted alkoxyls having from 1 to 18 carbon atoms; • d is equal to 1, 2 or 3; and - a peroxide crosslinking system. - a copolymer A based on at least one ethylene monomer and on at least one vinyl acetate monomer; - a reinforcing inorganic filler comprising silica; - as agent for coupling between said copolymer A and said reinforcing inorganic filler, an organosilane compound of formula B-Z-Si(G 1) (3-d) (G 2) (d) in which: • B represents a functional group interacting with the copolymer A, the group B being chosen from vinyl groups, halogen atoms, unsaturated α,β-enones, acryloxy groups, methacryloxy groups, acrylamido groups, methacrylamido groups and amino groups, • Z represents a spacer group formed of a divalent hydrocarbon-based chain comprising from 1 to 18 carbon atoms and making it possible to connect the group B to the silicon atom; • G 1, which are identical or different, each represent a monovalent hydrocarbon-based group chosen from linear or branched alkyls having from 1 to 18 carbon atoms, substituted or unsubstituted cycloalkyls or aryls having from 5 to 18 carbon atoms, substituted or unsubstituted alkenyloxyls having from 2 to 18 carbon atoms, substituted or unsubstituted aryloxy or aralkyloxy groups having from 6 to 18 carbon atoms, or a monovalent group in the form R 1 -(-O-(CJ 2) a) b -O- in which J represents a hydrogen, a phenyl group or an alkyl group having from 1 to 4 carbon atoms, b is an integer within the range 1 to 18 and a is an integer within the range 1 to 6, and R 1 being chosen from linear or branched, substituted or unsubstituted alkyls having from 1 to 4 carbon atoms or linear or branched, substituted or unsubstituted alkoxyls having from 1 to 4 carbon atoms, • G 2, which are identical or different, each represent a monovalent group chosen from the hydroxyl (-OH) group, linear or branched, substituted or unsubstituted alkoxyls having from 1 to 18 carbon atoms; • d is equal to 1, 2 or 3; and • B represents a functional group interacting with the copolymer A, the group B being chosen from vinyl groups, halogen atoms, unsaturated α,β-enones, acryloxy groups, methacryloxy groups, acrylamido groups, methacrylamido groups and amino groups, • Z represents a spacer group formed of a divalent hydrocarbon-based chain comprising from 1 to 18 carbon atoms and making it possible to connect the group B to the silicon atom; • G 1, which are identical or different, each represent a monovalent hydrocarbon-based group chosen from linear or branched alkyls having from 1 to 18 carbon atoms, substituted or unsubstituted cycloalkyls or aryls having from 5 to 18 carbon atoms, substituted or unsubstituted alkenyloxyls having from 2 to 18 carbon atoms, substituted or unsubstituted aryloxy or aralkyloxy groups having from 6 to 18 carbon atoms, or a monovalent group in the form R 1 -(-O-(CJ 2) a) b -O- in which J represents a hydrogen, a phenyl group or an alkyl group having from 1 to 4 carbon atoms, b is an integer within the range 1 to 18 and a is an integer within the range 1 to 6, and R 1 being chosen from linear or branched, substituted or unsubstituted alkyls having from 1 to 4 carbon atoms or linear or branched, substituted or unsubstituted alkoxyls having from 1 to 4 carbon atoms, • G 2, which are identical or different, each represent a monovalent group chosen from the hydroxyl (-OH) group, linear or branched, substituted or unsubstituted alkoxyls having from 1 to 18 carbon atoms; • d is equal to 1, 2 or 3; and - a peroxide crosslinking system.