Rubber composition vulcanizable with sulfur and tire tread and tire casing comprising the composition, characterized in that the composition comprises: a) at least one polymer selected from the group consisting of diene polymers, olefin/monomeric diene copolymers and isoolefin/halogenated para-alkylstyrene copolymers; b) silica as filler; c) at least one agent of the sulfur-containing silane type promoting the linkage between silica and polymer; d) at least one substituted guanidine; and in that it has at least one of the following characteristics: It has at least one diene polymer which comprises at least one terminal amino group of an aliphatic or cycloaliphatic amine which is bonded thereto at the end of the chain, the polymer then being devoid of the alkoxysilane and silanol group; the composition comprises at least one free aliphatic or cycloaliphatic amine.