Polling stations across the country are reporting a "steady flow of voters", but turnout is so far down on the General Election earlier this year.
Many regions experienced worse than average interest throughout the day despite the record seven candidates in the race.
Independent candidate Sean Gallagher voted early at Blackrock National School in Dundalk, Co Louth, with his wife Trish.
Labour’s Michael D Higgins cast his ballot with his wife Sabina Coyne and their sons Daniel and Michael Jnr in Bushy Park National School, Galway city, while Gay Mitchell voted at Kildare Place Primary School, Upper Rathmines Road, south Dublin.
Senator David Norris voted at Marlborough Street in the north of the city, a walk from his home, Mary Davis at Burrow School, Howth Road, Sutton, also north Dublin, and Dana Rosemary Scallon near her home in Claregalway, Co Galway.
Sinn Féin’s Martin McGuinness has no vote but accompanied party colleague, Donegal South West TD Pearse Doherty, as he voted in Bunbeg, Co Donegal.
Indications from polling stations nationwide suggested that turnout would be nowhere near the high 70% seen at the February general election.
Early figures put the percentage vote somewhere in the mid-20s, although indications in the early evening were that things were picking up as voters finished work and headed to their local polling stations.
The first results from the first counts in the 43 constituencies are expected early tomorrow evening or, depending on the final turnout, later that night.
While a formal declaration by the Presidential Returning Officer is not expected until Saturday, the voting pattern should be clear much earlier and the final outcome known late tomorrow night.
Joe Costello, director of elections for Labour’s Higgins, urged voters to get out and exercise their right.
“The next president will play a crucial role in restoring morale and confidence in Ireland, and rebuilding our reputation abroad,” he said.
Mr Gallagher, with wife and “secret weapon” Trish in Blackrock, said he never had any second thoughts about running but would not be drawn on whether a career in politics beckons if the tilt at the presidency fails.
“It’s been a tough 72 hours but it’s unfortunate what the campaign ended being about in the last couple of days,” he said.“
“I’m going to take one step at a time. I think we have plenty to focus on in the next 48 hours and I think one campaign at a time is enough, thanks.”
Mr McGuinness said he hoped people would use their vote to deliver political change.
“Many people have yet to vote,” he said.
“I would encourage each and every person with a vote to use it. This is your chance to usher in change in Ireland.”
About 3.1 million people are eligible to vote in the single transferable vote system, where the successful candidate needs 50% of the vote plus one.
Ireland’s ninth president follows the respected two terms, totalling 14 years, of Mary McAleese. She leaves office on November 10 after a remarkable tenure marked by her “Building Bridges” theme and work on the peace process in the North.
Mrs McAleese's time in office also saw Áras an Úachtaráin opened to more guests and visitors than ever before.
Counting of ballots begins tomorrow at 9am in 43 constituencies across the country with results relayed to a central database in Dublin Castle.
If the pattern of opinion polls in the final week stands up to the test, no candidate is likely to be within 10% of the 50% plus one majority.
The electorate is also being asked to vote on two referendums to make alterations to the Constitution.
One is on a proposal to beef up the powers of parliamentary committees in holding inquiries into matters of public interest, while the other would allow the government to reduce the pay of judges.
Voters in west Dublin are also casting ballots to fill the seat of the late former finance minister Brian Lenihan.