A rubber composition is 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, said inorganic filler comprising silica; as agent for coupling between said copolymer A and said reinforcing inorganic filler, an organosilane compound of formula (I) B-Z—Si(G1)(3-d)(G2)(d)  (I), wherein B, Z, G1, G2 and (d) have the meanings indicated in the claims; 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.