More than 3.2m people were asked whether they wanted to amend the country's constitution to allow gay and lesbian couples to marry.
Polling stations closed at 22:00 BST on Friday and counting started at 09:00 BST on Saturday morning.
An "unusually high" turnout was reported on Friday.
If the change is approved, Ireland would become the first country to legalize same-sex marriage through a popular vote.
Irish state broadcaster RTÉ said the turnout in most areas was well ahead of what it had been in recent referendums.
Dublin, Limerick and Waterford passed the 60% electorate turnout mark, while in Cork, Carlow, Kilkenny, Donegal, Tipperary, Kerry and Galway it was above 50%.
The upper courtyard of Dublin Castle will be open to 2,000 people on Saturday for people to view the declarations on a large screen on a first come, first serve basis.
A result is expected by mid to late afternoon on Saturday.
Prior to Friday, votes had already been cast in some islands as well as hospitals, hospices and nursing homes. Irish citizens who are registered are allowed to vote, but there is no postal voting. Many people returned to Ireland to cast their votes.
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