The two-day election is the first since the frontrunner Abdel Fattah al-Sisi deposed Islamist president Mohamed Morsi in July, a move that unleashed the bloodiest violence in Egypt's recent history.
Morsi's Muslim Brotherhood is boycotting the vote, as are revolutionary youths 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.
"The entire world is watching us, how Egyptians are writing history and their future today and tomorrow," Sisi said.
"Egyptians must be reassured that tomorrow will be very beautiful and great," he said, as supporters shook his hand and kissed his cheeks.
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.
Since the revolution, the country of 86 million people has been rocked by sporadic unrest and a tanking economy.
"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 Yusef, a 29-year-old lawyer waiting to vote in Cairo.
Yusef said he had voted for Sabbahi in the 2012 election that Morsi won, but that he would now back Sisi.
"We need someone strong, a military man," he said.
Sisi has said "true democracy" would take a couple of decades, and suggested he would not tolerate protests disrupting the economy.
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