A rubber composition is based on at least: a copolymer A, with a content of greater than or equal to 50 phr, said copolymer A being a copolymer based on at least one ethylene monomer and on at least one vinyl acetate monomer a reinforcing inorganic filler as agent for coupling between said copolymer A and said reinforcing inorganic filler, a copolymer B different from said copolymer A, said copolymer B being a copolymer based on at least one alpha-olefin monomer and on at least one functional monomer Y; and a peroxide crosslinking system. This composition is especially intended for the manufacture of semi-finished products for tires or for the manufacture of tires.