The actress played Ophelia opposite Olivier in his 1948 adaptation of Hamlet and she famously starred alongside Marlon Brando in the 1955 musical Guys and Dolls, for which she won a Golden Globe. Simmons' work in Hamlet earned her an Academy Award nomination for best supporting actress. She received a second Oscar nomination (for best actress) for 1969's The Happy Ending. Simmons' other film work included The Robe, The Actress and Spartacus.
Beyond the big screen, Simmons starred in the Stephen Sondheim musical A Little Night Music, with which she toured across the country and also brought the production to London.
Later in her career, she appeared on TV shows such as Murder, She Wrote and Star Trek: The Next Generation following her Emmy-winning turn in the 1983 TV miniseries The Thorn Birds. She had recently voiced the grandmother character in Howl's Moving Castle.
In 1987, Brooks told People magazine, "Every man I would meet would say to me, 'I have always loved your wife,'" who was considered one of the great screen beauties of her generation.
Simmons is survived by her daughters, Tracy Granger and Kate Brooks.