Born in Zagreb in 1914, Šulek began his music study very early by learning piano, violin, and composition.
He was also an active chamber music performer of the highest level, as he was the first violin of the Zagreb String Quartet from 1936 to 1938 and was a member of the Maček-Šulek-Janigro Trio from 1939 to 1945.
He launched a successful conducting career in building up an international reputation for the Chamber Orchestra of the Zagreb (now Croatian) Radio and Television.
In his teaching career, Šulek was a distinguished professor of musical composition and mentor of many leading Croatian composers.
his students including Milko Kelemen, Stanko Horvat, Krešimir Šipuš, Sandro Zaninović, Pavle Dešpalj, Dubravko Detoni, Igor Kuljerić etc.