Allowing gay couples to wed would be a seismic change in a country where homosexuality was illegal until 1993, and where abortion remains against the law except where the mother's life is in danger.
State broadcaster RTE said polling stations were recording a higher turnout than usual for referendums, with voting levels in some areas predicted to top 60 percent, more comparable with that witnessed at general elections.
Voters had until 10:00pm (2100 GMT) today to cast their ballots, with the result expected tomorrow afternoon.
"Today in fact is our first anniversary of our civil partnership and we hope it's our last anniversary as well because we would like to get married," he told AFP.
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At a polling station in the south Dublin suburb of Milltown, Rachael Stanley, 60, said she voted "No" and felt "strongly about it".
"This is about children. It's far too radical a step. I want to protect marriage and the stability of children," she told AFP.
If the move is approved and the ensuing legislation is passed, Ireland would become the first country to make the change following a popular vote.
Referendums in Croatia and Slovenia both resulted in "No" votes, although Slovenia's parliament went ahead and approved gay marriage in March.
"We are saying here, in a world first, that the people of Ireland can extend the right of civil marriage to all our citizens," Prime Minister Enda Kenny said this week.
Kenny voted at a school in County Mayo on the west coast, while President Michael D. Higgins cast his ballot in a hospital in Dublin's Phoenix Park.
Across the border in Northern Ireland, gay marriage is banned even though it is legal in the rest of the United Kingdom.
All Ireland's main political parties, including conservatives, support amending the constitutional definition of marriage, and the final polls put their camp comfortably in the lead.