Mathias Jung won the silver medal with the biathlon relay at the 1980 Lake Placid Winter Olympics together with Frank Ullrich, Klaus Siebert and Eberhard Rösch, finishing behind the Soviet Union. He also placed 21st over 10 km. In 1981 and 1982 Jung became World Champion in the relay, adding a silver medal one year later, always running the first leg. Domestically he won a silver medal in 1980 and a bronze medal in 1979 in the 10 km, as well as two titles in 1981 and 1982 in the relay, and three silvers in 1978, 1979 and 1983 with ASK Vorwärts Oberhof.
Educated as an electrician, Jung later worked in a ski workshop at Schmalkalden. During his sport career he was employed by the Nationale Volksarmee (NVA).