Yury Mukhin made his international début at the 1992 Olympics, where he swam in the heats for the Unified Team’s 4×200 freestyle relay team that went on to win an Olympic gold. At the 1993 European Championships Mukhin, now swimming in the final, won gold in the 4×200 freestyle relay and, at the 1994 World Championships, won silver in the same event. At the 1995 Universiade Mukhin won bronze in the medley relay. Domestically, Mukhin won Soviet 4×200 free relay titles in 1990-91. After finishing his sporting career in 1996, Mukhin worked as a swimming coach and sports administrator in Omsk.
Personal Bests: 50 m freestyle – 23.77 (1995); 100 m freestyle – 51.37 (1995); 200 m freestyle – 1:50.36 (1993).