A series of leaked papers show the two biggest banks in the country helped certain people avoid paying tax by using offshore accounts.
Both Bank of Ireland and AIB say they no longer use the tax havens as outlined in the Paradise Papers.
The revelations have prompted calls for the Government to outline how much it knew about the banks offshore activities and the wealthy individuals who were able to avoid paying tax as a result.
U2 frontman Bono is among those listed in the documents, which reveal investments in offshore accounts.
The singer, who is listed under his full name Paul Hewson, owned shares in a company registered in Malta that invested in shopping centre in Lithuania, company records show.
A spokeswoman said Bono was a "passive, minority investor" in the Malta company that closed down in 2015.
The papers, from the International Consortium of Investigative Journalists (ICIJ), also allege that one offshore investment leads to US President Donald Trump's commerce secretary, Wilbur Ross.
The papers claim he has a stake in a shipping company that has received more than US$68m (€58.5m) in revenue since 2014 from a Russian energy company co-owned by the son-in-law of Russian President, Vladimir Putin.
The records expand on revelations from the leak of offshore documents that spawned the 2016 Panama Papers.
The ICIJ say the new files "shine a light on a different cast of underexplored island havens" - including the Cayman Islands and Bermuda.
In response to the documents, Taoiseach Leo Varadkar says Ireland is fully compliant with tax transparency.
Children's Minister Katherine Zappone says the Government will get tough with financial institutions on the issue of tax justice.
Britain's Queen Elizabeth II also features in the documents.
Her private estate has allegedly invested millions of pounds in offshore tax havens.
While the Queen's private estate - the Duchy of Lancaster - provides some details of its investments in UK property, it has never disclosed details of its offshore investments.
German newspaper Suddeutsche Zeitung alleges that in 2005, the Duchy of Lancaster invested USUS$7.5m (€6.4m) in Dover Street VI Cayman Fund.
The Cayman Islands charges no direct tax on the earnings made by companies operating in the territory.
Britain's Queen Elizabeth II | File photo
Suddeutsche Zeitung also alleged that Dover Street further invested in a subsidiary company called Vision Capital Partners VI B LP to buy into two UK retail chains, one of which was BrightHouse.
BrightHouse is the UK's largest rent-to-own firm and has been accused by a UK parliamentary committee of charging inflated prices to some of the poorest people in the country.
"Yes, the Duchy was aware that the Jubilee Absolute Return Fund was run offshore," said Chris Addock, chief finance officer of the Duchy of Lancaster.
A spokesperson for the Duchy of Lancaster said: "We operate a number of investments and a few of these are with overseas funds. All of our investments are fully audited and legitimate.
"The Dover Street investment was bought in 2005 and forms only 0.3% of the total value of the Duchy.
"The Duchy's investment in BrightHouse is through a third party and equates to stg£3,208 - just 0.0006% of the Duchy's value.
"The Queen voluntarily pays tax on any income she receives from the Duchy."
Anti-monarchy groups said the revelations showed Queen Elizabeth II must be open and transparent about her investments and the tax she pays on them.
Other royals and politicians with newly disclosed offshore ties include Queen Noor of Jordan, Uganda’s foreign minister and a former UN General Assembly president Sam Kutesa, Brazil’s finance minister Henrique de Campos Meirelles and Lithuanian member of the European Parliament Antanas Guoga.
There is nothing to suggest that any of the investments are illegal.
Additional reporting: IRN