A rubber composition usable for the manufacture of tires, based on at least one diene elastomer, a reinforcing inorganic filler and a coupling agent providing the bond between the inorganic filler and the elastomer, wherein said inorganic filler comprises a silicon carbide having the following characteristics: (a) a BET specific surface area of between 20 and 200 m.sup.2/g; (b) an average particle size (by mass), d.sub.W, of between 10 and 350 nm. Tires or semi-finished products for tires such as treads comprising said rubber composition.