Some exhibits had been sealed pending jury selection, which was completed Tuesday night. But the jury had not yet been sworn in, the San Angelo Standard-Times reported.
Jeffs, head of the Fundamentalist Church of Jesus Christ of Latter Day Saints, a Mormon splinter group, is charged with sexual assault of a child in 2005 and aggravated sexual assault of a child in 2006 for having married a 12-year-old girl and fathering a child with her. He could face 119 years in prison if convicted.
One of Jeffs' first accusers, Elissa Wall, told ABC Wednesday morning the trial "will shock the world."
"This is an opportunity for people to see firsthand the actual crimes that Warren Jeffs himself has committed," she said.
Wall was one of the first of Jeffs' followers to press criminal charges when, at age 14, she said he forced her to marry her 19-year-old first cousin, Allen Steed.
Jeffs was convicted of sexual assault in the case, but the verdict was reversed on a technicality.
Wall is now in her early 20s and married with two children.