Biles received a score of 13.100, tied with U.S. teammate Suni Lee for fourth.
There was an extended wait for her score to post. At one point, Biles rolled her eyes in seeming annoyance knowing she wasn't going to finish on the medal stand.
Alice D'Amato of Italy took the gold with a score of 14.366. Zhou Yaqin of China earned silver with a 14.100, just ahead of bronze medalist Manila Esposito of Italy. Italy, which won silver behind the U.S. in the team competition, had never medaled on beam before.
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Biles finished in a tie for fifth with Lee, whose hopes for a gold on beam she's long coveted ended in the middle of her routine when she fell during the end of her acro series, just like Biles did a few minutes later.
The 21-year-old Lee will still leave Paris with three medals just months after she was bedridden while trying to navigate a pair of chronic kidney-related diseases.
While Lee's Olympics are over, Biles is also in the floor final later Monday, an event where she's never lost a major international competition, including a gold in Rio do Janeiro eight years ago.
“We were both just kind of annoyed just because we know what we’re capable of,” Lee said. “We weren’t able to get it done today, but she still has floor and she’s the G.O.A.T., so she’ll be amazing.”
There is plenty of history on the line for Biles in what could be the last competition of her career. Biles has 10 medals in her Olympic career, including seven golds. A medal in the floor final would tie her with Czechoslovakia's Vera Caslavska for the second-most medals by a female gymnast in Olympic history, trailing only former Soviet Union great Larisa Latynina's 18.