An object of the present invention is to provide an SBR composition for a torsional damper in which the SBR composition has a good physical property balance of high load-bearing properties, low CS properties, and the kneadability and roll processability of a rubber material, and to provide a torsional damper. The object is achieved in such a manner that the SBR composition for the torsional damper comprises at least: (a) an SBR polymer having a combined styrene content of 10 wt % to 50 wt %; (b) carbon black comprising FEF grade carbon black and HAF grade carbon black blended at a ratio of FEF:HAF=1:3 to 3:1; (c) a crosslinking system including sulfur, a sulfur-donating compound, and an organic peroxide compound; and (d) a co-crosslinking agent, wherein 60 parts by weight to 100 parts by weight of the carbon black as total parts by weight of the FEF grade carbon black and the HAF grade carbon black is blended based on 100 parts by weight of the SBR polymer, 0.4 part by weight to 2.5 parts by weight of the sulfur is blended based on 100 parts by weight of the SBR polymer, the sulfur-donating compound is blended at 0.625 time to 12.5 times the blending amount of the sulfur, the organic peroxide compound is blended at 1.25 times to 12.5 times the blending amount of the sulfur, and 4 parts by weight to 16 parts by weight of the co-crosslinking agent is blended based on 100 parts by weight of the SBR polymer.