The company did not immediately respond to a request for comment by The Associated Press.
Tara Booth, Mississippi Department of Corrections spokeswoman, said the department had not been served with the complaint and would respond to the allegations in court.
The complaint said the prison houses some of the state's most severely mentally ill prisoners, including juveniles, and many of them aren't receiving proper care. A 16-year-old inmate was put in a cell with an adult and sexually assaulted, the lawsuit said.
The lawsuit also said rapes, stabbings and beatings were "rampant."
"Prisoner-on-prisoner stabbings and beatings are frequent because the locking mechanism on the cell doors can readily be defeated, and some officers are complicit in unlocking doors to allow violence to occur," the lawsuit said.
Some prisoners are denied care for so long that they set fires in their cells to get attention, the lawsuit said. It also said broken toilets force some prisoners to use the restroom on trays or in plastic bags, which they then toss through slots in their cell doors.
The lawsuit said rats climb over prisoners' beds and some inmates put the rodents on makeshift leashes to sell as pets to mentally ill prisoners.
The prison has a capacity of 1,362 male inmates and is run by Management and Training Corp., based in Centerville, Utah.
MTC is not named as a defendant. The company did not immediately respond to a request for comment.
The lawsuit said a prison official ignored one inmate's pleas for help until one of his testicles swelled to the size of a softball in June 2012. By the time he received an ultrasound, testicular cancer had spread to his abdomen, the lawsuit said.
During a news conference Thursday, Jody Owens, a Mississippi-based lawyer for the SPLC, called conditions at the prison "a shock to the conscience of a humane society."
"Enough is enough," Owens said. "It is time to stop the abuse of our loved ones, our brothers, our sons and fathers."
Owens said advocates asked to meet with the state more than a year ago about conditions but he said they declined.
Terry A. Kupers, a psychiatrist who studied the facility for the ACLU, issued a report in February 2011 that said inadequate staffing, poor mental health programs and an overburdened prison psychiatrist were major problems.
Some mentally ill patients tried to avoid the prison psychiatrist for fear of being injected with powerful drugs that made them vulnerable to thefts and attacks, while others saw their diagnosis downgraded and were taken off medications, Kupers' report said.
Kupers also said the inmates aren't getting enough food.
"All inmates report significant weight loss since arriving at EMCF, from ten to 60 pounds, and from my direct observation it is clear that all the men are much thinner, almost emaciated, in comparison to old snapshots I viewed in their charts or on their identity cards showing them much heavier" Kupers wrote.
Associated Press writer Jeff Amy contributed to this report.
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Due to a Salt Lake Tribune editing error, an earlier online version of this article incorrectly stated Management Training Corp. is a defendant in the lawsuit. MTC operates the prison, but is not a defendant.