A silica-containing rubber mixture is produced from a rubber, a sulphur-containing alkoxysilane, a crosslinking agent, a silica-containing filler, and 0.1 to 15 parts by weight, based on 100 parts by weight of the rubber, of a silicon-free polysulphide additive of the formula (I) A-S-(S)x-S-B where x is 0-4, and A and B are the same or different, are alkyl or aryl, and contain at last one oxygen, which may be in the form of a carboxyl group.