Angela Sdrinis Legal, which lodged the class action in the Supreme Court of Tasmania, alleges staff used degrading strip-search procedures and isolation and beatings as punishment tools.
The firm says the claim alleges staff at the Ashley Youth Detention Centre encouraged detainees to attack each other, and left younger or female inmates unsupervised and unprotected against older male inmates.
It also alleges the plaintiffs were subject to systemic negligence at the centre in the state's north as early as 1961 and as recently as 2019.
The state government in September announced the facility would be closed within three years, after allegations of child sexual abuse became public.
A commission of inquiry into child sexual abuse in Tasmania's public institutions, set up partly in response to allegations made against detention centre staff, will next week begin hearing evidence about the centre.
The law firm says four lead plaintiffs are seeking damages for themselves and more than 100 other former detainees.
"The history of (the detention centre), in its various names, is notorious and tragic," lawyer for the plaintiffs, Angela Sdrinis, said in a statement.
"The Supreme Court class action will seek proper compensation according to modern legal standards."
A spokesman for the state government said it could not comment due to the flagged legal action.
"The commission of inquiry will be examining the (centre) in the upcoming hearings and we will not hesitate to act where required to ensure our children and young people are safe," he said.
It has previously said all current detainees are in a safe environment.
Four former detainees last month launched individual Supreme Court claims, alleging physical and sexual abuse at the facility in the 1990s and 2000s.
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