Radek Ťoupal spent almost his entire hockey career playing with HC České Budějovice in Czechoslovakia and the Czech Republic. He was with that team from 1982-90 and 1993-2000. He also played in Europe with Dukla Trenčín in the Czech leagues in 1990-91, HPK Hämeenlinna in the Finnish league (1991-93), Starbulls Rosenheim in 1994-95 in Germany, and he finished his career with Kapfenberg EC in Austria in the 2000-01 season. Ťoupal was drafted in the 6th round by the Edmonton Oilers in the 1987 NHL Entry Draft, but never played professionally in North America. A forward, he was a solid scorer in the European leagues, appearing in over 700 games, and scoring about 300 goals and 800 points – some of his early years are not well documented. Internationally Ťoupal played for Czechoslovakia at the 1986 World Junior Championships, the 1991 World Championships, and the 1992 Winter Olympics. He skated for the Czech Republic at the 1993 Worlds and 1994 Winter Olympics.