Certain girls were targeted by those boys, and "it was usually a girl that was especially vulnerable because she was alone at the party or shy," Swetnick claimed.
Swetnick said she "witnessed efforts by Mark Judge, Brett Kavanaugh and others to cause girls to become inebriated and disoriented so they could then be 'gang raped' in a side room or bedroom by a 'train' of numerous boys."
"I have a firm recollection of seeing boys lined up outside rooms at many of these parties waiting for their 'turn' with a girl inside the room," Swetnick said. "These boys included Mark Judge and Brett Kavanaugh."
She also said in her affidavit sent to the Senate Judiciary Committee that in approximately 1982 "I became the victim of one of these 'gang' or 'train' rapes where Mark Judge and Brett Kavanaugh were present."
"Shortly after the incident, I shared what had transpired with at least two other people," Swetnick said.
"During the incident, I was incapacitated without my consent and unable to fight off the boys raping me. I believe I was drugged using Quaaludes or something similar placed in what I was drinking."
She says that she shared the story of her own rape with "at least two other people" shortly afterward.
Avenatti told MSNBC that "My client has been issued a number of security clearances by the federal government over the years. She has been fully vetted time and time again, and she is an honest and courageous woman."
"And I'm going to caution Donald Trump, Brett Kavanagh, [Senate Judiciary] Chairman [Chuck] Grassley and others, if they try to come after my client or engage in some smear campaign, they better pack a lunch because we're going to respond twofold," Avenatti said.
"We are going to respond double as it relates to force. So they better be very careful before they start spewing nonsense and trying to call my client a liar."
A spokesman for Grassley, R-Iowa, said the committee's lawyers "are in the process of reviewing" Swetnick's affidavit.
Senate Minority Leader Chuck Schumer, D-N.Y., said he believed Kavanaugh's nomination should withdrawn, or that Trump should order the FBI to reopen its background check investigation of the judge.
"There are now multiple, corroborated allegations against Judge Kavanaugh, made under penalty of perjury, all of which deserve a thorough investigation," Schumer said.
Sen. Patty Murray, D-Wash., called Swetnick's allegations "horrifying."
"It is important to note that it is an affidavit and she has signed it under [penalty of perjury]. So people don't do this randomly. It needs to be investigated, absolutely," Murray said during an interview with MSNBC.
"I believe that there are responsible Republicans who are going to share the view that it is not just a Supreme Court nominee that is on trial right now. It is the United States Senate."
Before he took Swetnick's case, Avenatti already was well-known as the attorney for Stormy Daniels, the porn star who says she had sexual affair with Trump in 2006, months after his wife Melania gave birth to their son.
Daniels was paid $130,000 in hush money by Trump's then-personal lawyer, Michael Cohen, shortly before the 2016 presidential election that sent Trump to the White House.
Cohen last month pleaded guilty to tax crimes and to violating campaign finance law with the payment to Daniels, whose real name is Stephanie Clifford.
Cohen during his plea hearing told a judge that he had paid Daniels at the behest of Trump for the purpose of affecting the presidential election.
Trump, who has admitted reimbursing Cohen, has not been charged in the case.
Avenatti has said he is exploring a run for the presidency himself in 2020.
— Additional reporting by CNBC's
Download Swetnick's affidavit or read it here: