An object of the invention is to provide a block copolymer hydrogenation product suitable for a sheet and a heat shrinkable film which are excellent in solvent resistance, rigidity, elongation and transparency, which is excellent in a balance of physical properties such as solvent resistance, natural shrinkability, low-temperature shrinkability, rigidity, transparency and low-temperature elongation, and a composition thereof. The invention relates to a block copolymer hydrogenation product having a weight ratio of a vinyl aromatic hydrocarbon and a conjugated diene of 55/45 to 95/5, a number average molecular weight measured by gel permeation chromatography (GPC) of 30,000 to 500,000 and a hydrogenation rate of 30% or more, wherein the vinyl aromatic hydrocarbon incorporated into the hydrogenation product has a block rate of 60 to 98% by weight, wherein relative to the weight of the total vinyl aromatic hydrocarbon polymer blocks, the ratio of vinyl aromatic hydrocarbon polymer blocks having a molecular weight of 50,000 or less is 80% by weight or more and the ratio of vinyl aromatic hydrocarbon polymer blocks having a molecular weight of 15,000 or less is from 10 to 80% by weight, and wherein at least one peak temperature of function tan δ in a dynamic viscoelasticity measurement of the hydrogenation product is present within the range of exceeding −80° C. to lower than −10° C.