Born in Ufa, Soviet Union, Cherkasov first came to the tennis world's attention as an outstanding junior player. In 1987, he was ranked the World No. 3 junior player and finished runner-up in the boy's singles at the US Open (lost to David Wheaton in the final).
Cherkasov turned professional in 1988. In 1990, Cherkasov claimed his first top-level singles titles when he won the inaugural Kremlin Cup in Moscow, defeating Tim Mayotte in the final 6–2, 6–1. He also reached the quarter-finals of the 1990 Australian Open and US Open.
1991 saw Cherkasov successfully defend his Kremlin Cup title, saving two match points in a 7–6, 3–6, 7–6 win in the final against Jakob Hlasek. Cherkasov reached his career-high singles ranking of World No. 13 in June that year.
In 1993, Cherkasov saved three match points in 3-hour, 54-minute quarter-final victory over Italy's Andrea Gaudenzi at Tel Aviv, to win 6–7, 7–6, 7–5 in what was the longest best-of-three set match in tour history.
In the end, his two victories at the Kremlin Cup in Moscow proved to be the only top-level titles of Cherkasov's career. He retired from the professional tour in 2000, having earned prize-money totalling US$2,259,875.
|No.||Date||Tournament||Surface||Opponent in final||Score|
|1.||November 5, 1990||Moscow, Russia||Carpet (i)||Tim Mayotte||6-2, 6–1|
|2.||November 4, 1991||Moscow, Russia||Carpet (i)||Jakob Hlasek||7-6(2), 3-6, 7-6(5)|