Iraqi inmates were sexually assaulted, beaten, administered electric shocks and kept in cages or crates, the magazine said, based on 60 hours of interviews with 10 former inmates, including a 15-year-old boy.
Writer Donovan Webster quotes an inmate saying he was hung naked from handcuffs in a frigid room while soldiers threw buckets of ice water on him.
Webster added that several of the people he interviewed said their mistreatment took place in July, three months after the Abu Ghraib prisoner abuse scandal broke in late April.
The article said the former detainees interviewed are suing two American companies that provided translators and interrogators to forces in Iraq and that their firsthand accounts comprised "hundreds, if not thousands, of separate Geneva Conventions violations".
In one example cited in the article, a 15-year-old boy said he had been forced to crouch in a wooden crate for 11 days, wearing handcuffs and blacked-out ski goggles. He was then taken to the bathroom and sexually assaulted.
He said he was again sexually assaulted two days later in the prison north of Baghdad but let go later in the day when a soldier apologised to him for being illegally detained and gave him $50.
The magazine said the accounts of abuses were impossible to independently verify.
It quoted a US military spokesman for detainee operations in Iraq as dismissing the assertions that prisoners were held illegally, kept in wooden boxes, handcuffed and blindfolded and subjected to sexual threats, abuse and assault.