Russia's presidential election has seen a turnout of nearly 60%, officials say.
Voting in St Petersburg: The city was Mr Putin's launch pad
First deputy PM Dmitry Medvedev - the Kremlin's chosen candidate - is expected to easily beat his three challengers, correspondents say.
But the Kremlin wanted a good turnout to counter criticism that the vote was not fair.
Various inducements were offered to mobilise voters, including cheap food, free cinema tickets or toys, correspondents say.
There are also reports that many workers were told to vote by their bosses.
The election brings to a close Vladimir Putin's eight years in office.
Observers say the poll's outcome is not in doubt. Mr Medvedev, 42, the Kremlin's preferred candidate, has promised to make Mr Putin his prime minister.
The electoral commission chief, Vladimir Churov, said turnout was higher than in the December parliamentary election.
But the independent Russian election watchdog Golos has condemned what it sees as coercion to ensure a high turnout.
"There can't be a small turnout when people are forced to go to the polls," said Golos deputy director Grigory Melkonyan, quoted by the AFP news agency.
But Kremlin spokesman Dmitry Peskov said the turnout showed that many people "are choosing to vote for a continuation of the changes" made by Mr Putin.
The BBC's Richard Galpin in Vladivostok, in the Far East, says there was barely any campaigning by any of the candidates and little excitement amongst the electorate.
Medvedev media blitz
Mr Putin, hugely popular because of Russia's economic boom, was barred by the constitution from seeking a third term.
In the run-up to the vote Russia's main television channels gave generous coverage to Mr Medvedev, who refused to debate with his rivals.
The other candidates are: Communist Party leader Gennady Zyuganov, nationalist Liberal Democrat Vladimir Zhirinovsky and Democratic Party candidate Andrei Bogdanov.
More than 109 million Russians were registered to vote in the elections.
Voting closes in the western enclave of Kaliningrad at 1800 GMT on Sunday.
Pressure to vote
Mr Medvedev voted in Moscow, saying "spring has arrived - although it is raining, a new season has come".
Before his rise to power in the Kremlin he trained as a lawyer in St Petersburg, where he also worked alongside Vladimir Putin. But unlike Mr Putin, he has no background in the security services.
There has been very little scrutiny of voting by Western election observers, many of whom stayed away.
Civil servants were ordered by their managers to vote, and there are reports that police and teachers were under similar pressure, our correspondent in Vladivostok says.
A prominent critic of the Kremlin, former chess champion Garry Kasparov, told the BBC that support for Mr Putin and his allies was not self-evident.
"Mr Putin never stood for free and fair elections and when you talk about his big numbers they are obviously inflated by the pro-Kremlin polling organisations", he said.
The main European election monitoring body - the Organisation for Security and Co-operation in Europe (OSCE) - decided not to send a delegation.
It said the Russian authorities were planning to impose unacceptable restrictions on its work. The OSCE complained about Russian limits on the number of observers and on the duration of their stay.
In a sign of continuing unrest in the Caucasus, two bomb explosions targeted a police convoy on Sunday in the Russian republic of Dagestan.
Several people were reported injured in the attack in Khasavyurt, near the border with Chechnya.