The present invention relates to a rubber composition for a sidewall, a clinch and an insulation comprising 20 to 60 parts by mass of filler, 1.0 to 4.0 parts by mass of sulfur and 0.1 to 10 parts by mass of at least one vulcanization accelerating aid selected from a group comprising a citraconimide compound, an organic thiosulfate compound, an alkylphenol-sulfur chloride condensate, a compound represented by the formula (2) and a metal salt of methacrylic acid represented by the formula (3), based on 100 parts by mass of a diene rubber component comprising 10 to 70% by mass of at least one diene rubber component (a) selected from a group comprising a solution polymerization-modified styrene-butadiene rubber, a tin-modified butadiene rubber and a butadiene rubber whose terminal is modified with a compound represented by the formula (1), and 20 to 80% by mass of a diene rubber component (b) other than the diene rubber component (a) for the purpose of improving rolling resistance and steering stability.