Possessing a rich and warm voice, Cross sang a broad repertoire that encompassed works from a wide variety of musical periods and styles.
Impressed by his performance, composer Gian Carlo Menotti, who ran the Spoleto festival, invited Cross to portray the role of Donato in his new opera Maria Golovin.
In 1970–1971 he appeared as a guest at the Palacio de Bellas Artes in Mexico City and in 1971 he returned to the Spoleto Festival to portray the title role in Modest Mussorgsky's Boris Godunov.
He made his first appearance at the Glyndebourne Festival in 1976 singing the title role in Giuseppe Verdi's Falstaff, returning there the following year to portray Sir Morosus in Richard Strauss's Die schweigsame Frau.
In 1984 he portrayed Barbarossa in Verdi's La battaglia di Legnano with the Pittsburgh Opera and in 1987 he sang Wotan in Siegfried at the Art Park in Lewiston, New York.