Kamil Kašťák started his career with HC Litvínov in Czechoslovakia in 1988 but moved to the Finnish league in 1992, playing with HV71 Jonköping for one season, and then Lukko Rauma in the 1993-94 season. He returned to Litvinov during that season, and played for them again in 1996-97. In 1995-96 he split the season between ČKD Praha and HC Škoda Plzeň. Kašťák finished his career in Germany with two seasons with ES Weißwasser, retiring after the 1999 season. Internationally he played for Czechoslovakia multiple times, starting with the 1983 European Juniors, then in 1984-86 at the World Juniors. He played in the World Championships in 1992-94, winning a bronze medal with Czechoslovakia in 1992, and played for them at the 1992 Canada Cup.