Sexual abuse was endemic in boys' institutions and a chronic problem in some residential institutions, according to a new report.
The Commission to Inquire into Child Abuse states that sexual abuse of boys in the Artane Industrial School in Dublin and Letterfrack, Co Galway, was a chronic problem.
Its report has been published this afternoon - a decade after the commission was set up by the Government.
The report has strongly criticised the Department of Education for its handling of complaints about residential institutions.
It recommends that a memorial should be erected inscribed with the words of former Taoiseach Bertie Ahern when he issued an apology to the victims of abuse in 1999.
The Department of Education generally dismissed or ignored complaints of child sexual abuse and dealt inadequately with them according to the report.
Minister for Education and Science Batt O'Keeffe said that the Government would carefully study the findings and recommendations in the report.
Mr O'Keeffe extended his sympathy to those who were subjected to abuse while resident in industrial schools.
The report states that the safety of children was not a priority for the Christian Brothers who ran the institutions.
Cardinal Seán Brady welcomed the report this afternoon.
He said it documents a shameful catalogue of cruelty: neglect, physical, sexual and emotional abuse, perpetrated against children.
'I am profoundly sorry and deeply ashamed,' the Cardinal said, 'that children suffered in such awful ways in these institutions. Children deserved better and especially from those caring for them in the name of Jesus Christ.'
The report follows ten years of work by the commission which dealt with thousands of complaints from former residents of predominantly Catholic institutions.
It does not identify respondents and gives pseudonyms to those found guilty in a criminal trial.
The report says that the Christian Brothers Order was defensive in the way it responded to complaints and claims the order fails to accept any congregational responsibility for such abuse.
More allegations were made against the Christian Brothers than all of the other male orders combined.
A statement from the order read: 'We apologise openly and unreservedly to all those who have been hurt either directly or indirectly as a result of the deplorable actions of some Brothers, or by the inaction or inappropriate action of the Congregation as a whole.
'We are deeply sorry for the hurt caused. We are ashamed and saddened that many who complained of abuse were not listened to.
'We acknowledge and regret that our responses to physical and sexual abuse failed to consider the long term psychological effects on children.'
The report states that physical punishment in Artane in Dublin was excessive and children constantly felt under threat and were fearful.
Physical punishment was severe at Letterfrack
Letterfrack, according to the report, was an inhospitable, bleak, isolated institution in which physical punishment was severe, excessive and pervasive.
For two thirds of the period investigation in the Co Galway institution there was at least one sexual abuser present, according to the report.
Two abusers were present there for 14 years and the congregation offered no explanation of how they remained there undetected and unreported for so long.
The report describes how at St Joseph's Industrial School in Tralee, Co Kerry, a brother terrorised children for more than seven years after being moved there from a day school where his violence towards children was causing severe problems with parents.
The commission received thousands of complaints of emotional, physical and sexual trauma inflicted on children by Catholic priests, brothers and nuns.
More than 100 institutions, chiefly run by religious orders, including industrial schools, institutions for children with disabilities and ordinary day schools, were examined by the commission chaired by Mr Justice Seán Ryan.
It is over five years since the commission's first chairperson, Judge Mary Laffoy, signed its account of abuse and neglect endured by boys in the Catholic-run Baltimore Industrial School over 60 years ago in west Cork.
The Commission's Investigation Committee held more private than public hearings.
Earlier, the Taoiseach told the Dáil that the failures of the State and others charged with the care of children must be acknowledged and lessons learned.