Elsa Gress was born in Frederikshavn, Denmark. Her father lost money gambling and the family was forced to move frequently from one home to another. As a teenager in the 1930s, she went on walking tours in France and Nazi Germany, and in 1937, she began studying literature at Copenhagen University. During World War II, she was an active member of the resistance against the German Occupation of her country. She made her literary debut in 1947 with a volume of essays called Strejftog (Raids) and a novel, Mellemspil (Interlude), inspired by her wartime experiences and grief.
She had a liaison with R.W.B. Lewis, the American literary critic, with whom she had a son, David Gress. While in New York in 1952, she met Charles Clifford Wright, a painter, at the Yaddo Artists Colony near Saratoga Springs. In 1956, he joined her in Copenhagen, where they married and had two children together. Together with her husband, Elsa Gress created Decenteret, a collective artistic and cultural center in Glumsø, which attracted guests from around the globe to exhibitions, theatrical performances and lectures. Her first play, Philoctetes Wounded (1969) was written in English, with the Danish version, Den sårede Filoktet, published the following year. It was adapted for television in 1976, establishing her reputation as a playwright. Among her other works were further novels, short stories, radio plays, and essays. She published her memoirs in three volumes: Mine mange hjem (My Many Homes, 1965), Fuglefri og fremmed (Free as a Bird and a Stranger, 1971) and Compania 1—2 (1976). She was named a member of the Danish Academy in 1975.