After graduating in 1959, he became the youngest member to join the National Theatre, where he acted in Karel Čapek's The White Disease and Vilém Mrštík's Maryša.

His first American film role was in Ragtime (1981), directed by fellow Czech emigre Miloš Forman.

He played supporting parts in Reds (also 1981, directed by Warren Beatty), The Osterman Weekend (1983, Sam Peckinpah), 2010: The Year We Make Contact (1984, Peter Hyams), The Karate Kid Part III (1989, John G. Avildsen), Apt Pupil (1998, Bryan Singer), as well as guest appearances on Highlander: The Series (1996), and Highlander: The Raven (1999).

In 2005, he was nominated for the Czech Lion Award for Best Actor in Leading Role for his performance in the Jan Švankmajer film Lunacy.

Although he occasionally visited the Czech Republic, Tříska remained a permanent resident of the United States in Los Angeles, California.