A third accused, aged 19, was acquitted of attempted rape, oral rape and sexual assault. The men, who cannot be named for legal reasons, had pleaded not guilty to all the charges.
Mr Justice Paul Carney described the reactions of one man's family to the verdicts at the Central Criminal Court as a "full scale riot" which reduced one juror to tears.
He added: "This was a gross and serious contempt in the face of the court which challenges the very foundation of the administration of justice, terrifying jurors conscientiously doing their duty."
He said the jurors were left "terrified and apprehensive for their own safety" and that "grown men were weeping" as a result of the outburst.
After the verdicts were delivered, supporters of the two men shouted: "My child is innocent, he didn't do anything."
They shouted that the acquitted man was "the one that did everything", saying: "He's a pervert and a rapist. He beat her. He killed her."
Mr Justice Carney said the two women were the "ringleaders". He added that there should be many more people in the dock but only these two were arrested.
For contempt of court he sentenced the 14-year-old sister of one accused to four days imprisonment and the 58-year-old mother of the other accused to seven days imprisonment.
After a nine-day trial and just under three hours of deliberations the jury returned their unanimous verdicts on Wednesday, finding the two men guilty of carrying out the offences in Cork on September 13, 2009.
The two men were aged 16 and 18 when they picked up the 31-year-old victim, who was drunk and separated from friends after a night out, drove her down a country lane and carried out the assaults.