William Couper was born September 20, 1853 in Norfolk, Virginia, son of John Diedrich Couper and Euphania Monroe Couling Couper. He acquired an interest in sculpture from time spent at his father's company, Couper Marble Works.
After studying at the Cooper Institute in New York, Couper won a scholarship to the Royal Academy at Munich in 1875. Disliking the atmosphere in Munich, he took a place in the studio of Thomas Ball in Florence, Italy in the same year. Couper married Mr. Ball's daughter, Eliza Chickering Ball in 1878, and remained in Florence for over two decades, returning to New York to open a studio in 1897.
In 1901, Couper received a bronze medal at the Pan-American Exposition in Buffalo. His notable works include a series of thirteen heroic busts of scientists for the American Museum of Natural History, a relief sculpture for the Sailors' Memorial in Annapolis, a statue of Capt. John Smith at Jamestown, and a portrait bust of John D. Rockefeller.
Couper retired in 1913 and died later in 1942 in Easton, Maryland.