Modosyan started wrestling in 1968. In 1975, he moved to Krasnoyarsk and started training under the guidance of the honored coach of the USSR Dmitry Mindiashvili. From 1982 to 1987, Modosyan was a member of the Soviet national freestyle wrestling team. He came in first place at the 1985 Wrestling World Cup. Modosyan had his most successful year in 1986, when he won the gold medal at the 1986 World Wrestling Championships and 1986 Goodwill Games. He won his second silver medal at the 1987 European Wrestling Championships.