Greek and Turkish Cypriots are holding twin referendums on whether to reunite their island after 30 years.
Many Greek Cypriots are sceptical about the UN plan
The vote comes a week before Cyprus is due to join the European Union.
With voting brisk on both sides, the Turkish north looks set to back the UN reunification plan, but the Greek part is likely to reject it.
Both sides must approve the plan if it is to be implemented. If it fails, EU laws and benefits will apply only to the Greek Cypriot community.
Diplomats are worried that a Greek veto will put paid to years of international pressure to reconcile the two parts of the island, split since the 1974 invasion by Turkish troops.
Without being specific, both the US and the European Union have given notice to Greek Cypriots that, if they vote against, efforts will be made to end the isolation of Turkish Cyprus.
The BBC's Jonny Dymond says Turkish Cypriots' support for reunification effectively reverses a historical trend, which had cast them in the role of the rejectionists.
"I feel like a tourist in my own country. We don't get back what we had with this solution."
Katia, Greek Cypriot
The plan crafted by UN Secretary-General Kofi Annan envisages a loose federal structure for the island.
Many Greek Cypriots refugees who fled the Turkish assault would be allowed to return and recover some of the land they lost.
But the Greek side is unhappy that the plan limits their right to return, while allowing tens of thousands of Turkish settlers introduced since 1974 to remain. Turkish troops would also be allowed to maintain a reduced garrison on the island.
Greek Cypriot President Tassos Papadopoulos, who rejects the plan, cast his vote early on Saturday and urged people to respect the outcome.
"Whatever the result, there should be no jubilation, and no incidents to blacken this day. Greek and Turkish Cypriots deserve better days," he said.
"We are not ready to live together because of the war."
Aliye Kemal, Turkish Cypriot student
Mehmet Ali Talat, prime minister of the breakaway Turkish north, forecast an overwhelming "yes" vote from his side.
"If we say 'yes', we will not accept being enslaved by the 'no' of the Greek Cypriot," Mr Talat said.
"For us the most crucial thing is the lifting of embargoes."
The veteran Turkish Cypriot leader, Rauf Denktash, by contrast, is against the plan - though if the opinion polls prove correct, the latter leader's stance defies the wishes of his people.
He insisted he would not resign if the Turkish side voted for the plan.
The EU has criticised Mr Papadopoulos for urging his electorate to reject the UN proposals. which until recently he appeared to have been backing.
But Russia has come out in his favour, accusing the UN of granting too many concessions to the Turks.
Russia used its veto powers on the UN Security Council to block a proposal for a neutral force to help police the island, were it to be reunified.
The proposal's backers said it was intended to reassure Greek Cypriots that they would not face a threat from Turkish soldiers - but Russia argued it was an attempt to influence Saturday's vote.