Elizabeth, 23, began her testimony against Brian David Mitchell just after 11 a.m., The Salt Lake Tribune reported.
Speaking calmly, she recounted how she was seized from her bedroom at knifepoint in the early morning of June 5, 2002, and forced to march hours to an encampment at age 14, CNN reported.
Smart said she and Mitchell were met at the encampment by Mitchell's wife, Wanda Barzee, and a "marriage ceremony" followed.
She was the third witness to testify, following her mother Lois and younger sister Mary Katherine.
Mitchell, 57, was removed from the courtroom before opening statements Monday. He entered singing "In Memory of the Crucified," and U.S. District Judge Dale Kimball ordered him removed to view the proceedings remotely.
Lois Smart testified she met Mitchell in 2001 while shopping. Her children urged her to give the apparently down-on-his-luck man some money. She gave Mitchell her husband's number to contact about doing odd jobs at their home.
She also described being told of Elizabeth's disappearance by her younger daughter.
Mitchell is accused of accused of kidnapping Smart, who was 14, from her bedroom and repeatedly raping her. She was not found and reunited with her family until March 2003.
Earlier, defense attorney Parker Douglas was asked to restart his opening statement. He had been just 3 minutes into it Thursday when Kimball halted the proceedings so a change-of-venue request by the defense could be considered. The motion was rejected Friday.
Douglas recounted Mitchell's life story and long history of mental illness.
Celebrity Breakups and divorces of 2014 [PHOTOS]