TECHNOLOGY FOCUS - POLYMERS - Preferred Composition: The content of structural unit derived from the vinyl aromatic compound with respect to the mass of the hydrogenated block copolymer, is 37-50 %mass. Preferred Property: The hydrogenated block copolymer has melt flow rate of less than 0.5 g/minute, measured at 200 degrees C under 5 kgf load. EXAMPLE - Cyclohexane (in ml) (3400) as solvent, and sec-butyllithium (5.9) as an initiator having concentration of 10.5 weight% were added to the dried pressure-resistant container, and heated to 50 degrees C, in presence of nitrogen. Then, mixture (126) of isoprene and butadiene with the mass ratio of 50/50 was added, polymerized for 2 hours, and then styrene (206) was added and polymerized for 1 hour. Mixture (306) of isoprene and butadiene having mass ratio of 50/50 were added and further polymerized for 2 hours. Then, 5 weight% tetrahydrofuran solution of dimethyl phthalate (6.12 g) were added to the polymerized mixture, heated at 70 degrees C, and coupling reaction was carried out for 3 hours. Methanol (0.25) was added and polymerization reaction was stopped, to obtain polymerized reaction liquid containing block copolymer having polymer blocks (B1 and B2). The mass ratio of polymer block (B1) with respect to the total mass of the polymeric blocks (B1 and B2) was 0.29. Palladium carbon (23.4 g) as hydrogenation catalyst was added to the reaction liquid, and hydrogenation reaction was performed under hydrogen pressure of 2 MPa at 150 degrees C for 10 hours. The palladium carbon was removed by filtration, cooled, and the filtrate was concentrated and vacuum-dried, to obtain hydrogenated block copolymer. The obtained hydrogenated block copolymer had hydrogenation rate of 98.2%, styrene content of 39 wt.%, vinyl bond content of 3.2%, coupling rate of 78%, branch coefficient of 2.9, weight average molecular weight of 286300, ratio of weight average molecular weight with respect to the number average molecular weight of 1.29, and melt flow rate (MFR) of less than 0.5 g/10 minutes. Thermoplastic-elastomer composition containing obtained hydrogenated block copolymer, Diana-Process-Oil PW-32 (RTM: paraffin type process oil) and IRGANOX 1010 (RTM: hindered phenolic antioxidant) in mass ratio of 100:500:0.6, was prepared. The obtained composition had excellent fluidity. The molded product of elastomer composition had excellent compression-set property, weather resistance and flexibility.