A rubber composition, in particular intended for the manufacture of tires, based on at least a predominant elastomer, chosen from the group consisting of butyl rubbers, essentially unsaturated diene elastomers, essentially saturated diene elastomers and the mixtures of these elastomers, and a reinforcing filler, characterized in that the composition also comprises at least one inert filler chosen from silicon-based lamellar mineral fillers and a nonfunctionalized polyisobutylene oil, having a molecular weight of between 200 g/mol and 40 000 g/mol, present in a proportion of between 2 and 50 phe.