Modified block copolymer composition

A modified block copolymer composition comprising:

• (1) a modified block copolymer consisting of a polymer block A comprising primarily a vinyl aromatic hydrocarbon and a polymer block B comprising primarily a conjugated diene, or a hydrogenation product of the copolymer, and
• (2) at least one of fillers selected from the group consisting of silica-based inorganic fillers, metal oxides and metal hydroxides,
• wherein the molecular chain of the component (1) has at the terminals thereof a functional group having at least one group selected from the group consisting of a hydroxide group, an epoxy group, an amino group, a silanol group, and an alkoxysilane group;
• the component (1) has a content of the vinyl aromatic hydrocarbon of 5 to 95% by weight;
• the amount of the component (2) is 0.5 to 50 parts by weight based on 100 parts by weight of the component (1);
• and the component (2) has an average particle size in a dispersion of 0.01 to 2 μm.