Biden was in a different vehicle and wasn't involved in the accident.
Fleming said she was in a van with Flowers, Eruzione, as well as White House and Secret Service personnel. The motorcade was heading to a hockey game when the van was rear-ended.
Fleming said Biden had a physician traveling with him who tended everybody on the scene. They also were checked at a hospital as a precaution.
"It was a big, huge van. We were thrown really hard and Vonetta hit her head on the seat cushion in front of her," Fleming said.
The group never made it to the hockey game, but Fleming and Flowers later attended a figure skating competition, sitting in the row in front of Biden.
Olympic authorities said the accident happened shortly before noon. Fleming, Flowers and Eruzione were in the motorcade's next-to-last vehicle. After their van was struck, it hit the vehicle in front of it.
Scott Gordon, spokesman for the Integrated Security Unit, said the accident was possibly caused by poor road conditions and perhaps an oil slick. The accident remains under investigation.
Fleming won the gold medal at the 1968 Grenoble Olympics, and Flowers won gold at the 2002 Salt Lake City Games. Eruzione was the captain of the U.S. Olympic Hockey team that won the Miracle on Ice game against the Soviet Union in 1980.
"It was just a really jarring twist of the neck, but I think we're going to be OK," Fleming said. "I think I'll have a stiff neck tomorrow and stiff muscles."
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AP Sports Writer Anne M. Peterson contributed to this report.
