Martyniuk is a soloist of the National Academic Bolshoi Opera and Ballet Theatre of the Republic of Belarus. In 2009 he performed the role of Jose in the opera Carmen by Georges Bizet, a joint project of Odessa National Academic Opera and Ballet Theatre and the Supierz Music Production. In 2010 he sang the part of Jose while touring Japan with the company of the National Opera of Ukraine. Since 2011 Eduard Martyniuk has been a guest soloist of the Bolshoi Theatre of Russia.
His repertoire includes Vaudémont in Iolanta, Pinkerton in Madama Butterfly, Rodolfo in La Bohème, Jose in Carmen, Cavaradossi in Tosca, the Duke in Rigoletto, Radames in Aida, Vladimir in Prince Igor, Raman in The Grey Legend, etc.