Conjugated diene series rubber compositions

A conjugated diene series rubber composition comprising 100 parts by weight of a diene series rubber containing at least 30 parts by weight of a modified styrene-butadiene copolymer rubber (modified S-SBR) obtained by copolymerizing 1,3-butadiene and styrene at a weight ratio of 80:20-50:50 in a hydrocarbon solvent in the coexistence of an organolithium compound as an initiator and 0.01-0.3 mol per 1 gram equivalent of the organolithium compound of at least one alkali metal compound selected from alkali metal compounds represented by the following general formulae:

• R.sup.1 M, R.sup.2 OM, R.sup.3 COOM and R.sup.4 R.sup.5 NM
• (wherein each of R.sup.1, R.sup.2, R.sup.3, R.sup.4 and R.sup.5 is an akly group, a cycloalkyl group, an alkenyl group, an aryl group or a partially substituted group thereof, and M is Na, K, Rb or Cs) and then modifying an active terminal of the resulting copolymer with a modifier, and 30-80 parts by weight of carbon black having a specific surface area of nitrogen adsorption of not less than 70 m.sup.2 /g and a dibutyl phthalate absorption of 70-150 ml/100 g.