Andrei Cherkassov was an outstanding tennis player even in his youth. In 1987 he was number 3 in the juniors and was in the final of the US Open , which he lost to the American David Wheaton with 5: 7 and 0: 6. The following year he began his professional career. At the Challenger tournament in Nyon he reached the semifinals, in which he was defeated by Francisco Clavet . He was also appointed to the Soviet Davis Cup team and used against the Netherlands. He was able to win the games against Paul Dogger and Mark Koevermans both.
In 1989 he reached the final at the ATP tournament in Sydney at the beginning of the year , but was defeated by the American Aaron Krickstein in two sets. During the year he won the Challenger tournaments in Porto and Lisbon. At the end of 1990, he achieved his first success at an ATP tournament. In Moscow he beat Tim Mayotte 6-2 and 6-1 . He defended the title in 1991 against Jakob Hlasek and also reached the final of the doubles competition with Alexander Wolkow , which was lost to the German duo Eric Jelen and Carl-Uwe Steeb 4-6 and 6-7. At the 1992 Olympic Games in Barcelona, he joined the United Team for the Commonwealth of Independent States . In the individual semi-finals he was defeated by Jordi Arrese 4: 6, 6: 7, 6: 3 and 3: 6. Since the third place was not played, he shared the bronze medal with Goran Ivanišević .
In 1993 he was twice in the final of an ATP tournament. After that, his career was less successful. Cherkassov won the 1995 Challenger tournament in Singapore against Yasufumi Yamamoto and in 1996 the tournament in Daytona Beach against Tommy Haas .
From 1988 to the end of his career in 2000, he played 30 matches in the Davis Cup , of which he won 17.