The two-day election is the first since the frontrunner and former army chief Abdel Fattah al-Sisi deposed President Mohamed Morsi in July, a move that unleashed the bloodiest violence in Egypt's recent history.
Morsi's Muslim Brotherhood movement is boycotting the vote, as are revolutionary youth groups who fear Sisi is an autocrat in the making.
But the 59-year-old retired field marshall is expected to trounce his sole rival, leftist Hamdeen Sabbahi, amid widespread calls for stability.
Polling stations opened at 0600 GMT for 53 million registered voters, with Sisi arriving early at a Cairo polling station to cast his vote amid a throng of jostling reporters and supporters.
Many view the vote as a referendum on stability versus the freedoms promised by the Arab Spring-inspired popular uprising that ousted veteran strongman Hosni Mubarak in 2011.
The country of 86 million people has been rocked by sporadic unrest and a tanking economy since then.
Mubarak's successor, the Morsi, lasted only a year in power, winning the country's first democratic presidential election only to quickly alienate many Egyptians who held mass rallies demanding his resignation.
"We need someone who speaks in a determined and strong way. The Egyptian people are frightened by this and respect those who are like this," said Milad Hanna, a 29-year-old lawyer, as he lined up outside a polling station in Cairo.
Hanna said he had voted for Sabbahi in the 2012 election that Morsi won, but will now vote for Sisi.
"We need someone strong, a military man," he said.
Sisi has said "true democracy" would take a couple of decades to reach Egypt, and suggested he would not tolerate protests that he said disrupt the economy.
He has also pledged to wipe out the Brotherhood, which had won every election after Mubarak's overthrow after being banned for decades.
The movement is boycotting the election and said on Sunday it would not recognise the outcome.
"Forgery will never grant legitimacy to a butcher nor will it lessen the determination of revolutionaries," the Brotherhood said in a statement.
The vote, monitored by international and Egyptian groups, is not expected to be marred by widespread rigging.
The Brotherhood, now blacklisted as a terrorist group, has been decapitated in a police crackdown that has killed more than 1,400 people, including an estimated 700 protesters on one day in August.
Morsi himself has been detained and placed on trial.
Hundreds of soldiers and policemen have been killed in militant attacks since Morsi's overthrow, with the deadliest claimed by an al Qaeda-inspired group based in the restive Sinai Peninsula.
The military and police deployed heavily to secure polling stations.
Sisi has called for a high turnout in the election, billed by the military-installed authorities and the West as a milestone toward elected rule in the country.
"You need to go down now more than any other time in (the country's) history. Go down, show to the entire world that there are 40, 45 (million) or even more" voters casting their ballots, Sisi said as campaigning closed on Friday.
The presidential poll will be followed by parliamentary elections this year
Sisi's sole election rival Sabbahi, a veteran dissident, has vowed to defend the democratic aspirations of the 2011 revolt.
"We swear to God that symbols of corruption and despotism (from the Mubarak era) will not return," he said on Friday.
Sisi has raised fears that Egypt could see more repression than under Mubarak's regime.
"What tourist would come to a country where we have demonstrations like this?" he asked Egyptian newspaper editors.
"You write in the newspapers: 'No voice is louder than freedom of speech!' What is that?" he asked.
The interim authorities have justified the overthrow of Morsi by saying the army heeded mass street protests against the Islamist's single year of divisive rule.
The April 6 youth movement, which spearheaded the anti-Mubarak revolt and whose leader has been jailed, has called for a boycott of the election.
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