One of the 17-year-old girls, a Steubenville High School student, said the 16-year-old girl was having trouble walking but never appeared to pass out. The other 17-year-old girl said she had never seen her friend so intoxicated.
If convicted, Mays and Richmond, who deny any wrongdoing, could be held in a juvenile jail until they turn 21.
The Associated Press normally does not identify minors charged in juvenile court, but Mays and Richmond have been widely identified in news coverage, and their names have been used in open court.
They were charged 10 days after the party, after a flurry of social media postings about the alleged attack led the girl and her family to go to police.
Steubenville officials have protested that outsiders have unfairly criticized police handling of the case and have given Steubenville a black eye. Officials created a website to counter misinformation about the case, disputing, for example, the allegation that the police department is full of ex-football players from the local powerhouse team, nicknamed Big Red.
Hacker activists have publicized tweets and other social media postings made the night of the alleged rape, including a 12-minute video in which one student joked about it while others in the background chimed in.
The National Organization of Women has demanded that the student be charged under the state's failure to report law. Attorney General Mike DeWine has called the video disgusting but said the student didn't have firsthand knowledge of the alleged assaults.
Bob Fitzsimmons, a lawyer for the girl's family, said, "The family wants this matter over so they can move on with their lives and their daughter's healing."
Dozens of witnesses for both sides were expected to testify at the trial. Their testimony is considered crucial because the girl was severely intoxicated that night and appeared to be passed out at times, according to several witnesses.