He was prevented from competing by Soviet authorities as they expected the flag bearer to win a gold medal and believed that Medvedev would not be able to do that.

Medvedev retired in 1962 to become the head coach of the Soviet national weightlifting team.

He served as vice-president of the European (1969–1975) and International Weightlifting Federation (1969–1980), and in addition acted as a judge.

From 1997 until his death he headed the weightlifting department of the Russian State University of Physical Education, Sport, Youth and Tourism, his alma mater.

They had a son Aleksandr (born 1952), who headed the Khrunichev State Research and Production Space Center.