Ethiopians have flocked in numbers to cast their ballots in an election which is being regarded as a crucial test of the country's fledgling democracy.
The election is the third under the ruling EPRDF
Hundreds of people lined up at polling stations with some of the queues extending to adjacent streets.
Security has been tightened, but the chairman of the national elections board says voting is going on smoothly.
More than 300 foreign observers - in the country for the first time - are investigating claims of irregularities.
The poll has been marred by opposition allegations of harassment of its agents up to the eve of voting.
One of the main opposition groups, the CUD, said hundreds of election monitors had been arrested, and it threatened not to accept the results of the vote.
The government denies the allegations, saying opponents want to discredit the poll for political reasons.
The National Election Board head, Kemal Bedri, said he was taken aback by the accusations.
Twenty-six million Ethiopians are registered to vote in the election, which is widely expected to return the governing Ethiopian People's Revolutionary Democratic Front (EPRDF), to power for a third term.
About 35,000 polling stations opened across the country at 0600 local time (0300 GMT) - although people living in the south-eastern Somali Region will have to wait until August to mark their ballot papers.
The board says the area is so remote and inaccessible they need to organise a separate polling day.
In the capital, Addis Ababa, a stream of voters built up at polling stations in mid-morning.
"Although it is my wedding day, I don't want to miss the opportunity to vote," said Adane Abdi, quoted by Reuters news agency.
Former US President Jimmy Carter, heading an observer mission from his Carter Center, said he had found "very long lines of people waiting pleasantly".
Mr Carter said his team - as well as other observers - were investigating reports that 454 ballots had been found with an unclear irregular mark in central Addis Ababa and similar ballots outside the capital.
The National Election Board said the mark was a printing error.
And Prime Minister Meles Zenawi said people should await the reports of foreign observers before alleging any election abuse.
"If the international observers say the opposition won, we will accept that decision," Mr Meles said.
Mr Carter said there had been positive developments in the election process.
"Even opposition leaders we've met with have emphasised dramatic improvements in this country, the openness of the campaign," he said.
But a report this week by Human Rights Watch said that political repression in Oromia, one of the country's biggest regions, meant that democracy there was a hollow exercise.
Ethiopia's State Minister for Information, Netsannet Asfaw, said Human Rights Watch should check its facts.