Burian was born in Plzen, Czechoslovakia, where he came from a musical family. His father was an opera singer. E. F. Burian is the father of singer and writer Jan Burian. In 1927, he graduated from the Prague Conservatory, in the class of J. B. Foerster, but he began participating in cultural life much sooner. E. F. Burian was a member of Devetsil, an association of Czech avant-garde artists. In 1926-1927, he worked with Osvobozené divadlo, but after disputes with JindÅich Honzl, he and Jiri Frejka left the theatre. Later, they founded their own theatre, Da-Da. He also worked with the ModernÃ studio theatre scene. In 1927 he founded the musical and elocutionary ensemble Voiceband.
In 1923, he joined the Communist Party of Czechoslovakia. His work, strongly influenced by communist ideas, bordered on political agitation. In May 1933, he founded the D 34 theatre, with a strongly leftist-oriented program.
In 1941, Burian was arrested and spent the rest of World War II in German concentration camps at Theresienstadt, Dachau and finally in Neuengamme. He helped to organize illegal cutural programs for the inmates. After the war, he founded D 46 and D 47 theatre, and led theatres in Brno and the operetta house in Karlin. After Victorious February in 1948, he worked as a member of the Czechoslovak communist parliament. In the post-war time, he became one of the leading promoters of the communist cultural nomenclature. He attempted to reorganize theatres, with a goal of placing communists into leadership posts of theatres.
Burian died in 1959 in Prague.
His work was strongly influenced by dadaism, futurism and poetism, and was very leftist oriented. After the war, it was strongly agitative of Communist ideas. He had a strong influence on Czech modern theatre, and his innovative staging methods (work with metaphor, poetry, and symbols) and inventions (theatergraph, voiceband) are inspirational for the theatre even now.