The two-day election is the first since the frontrunner 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 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.
Sisi himself voted minutes after polling opened Monday amid a throng of jostling reporters and supporters. About 53 million people are eligible to vote.
"The entire world is watching us, how Egyptians are writing history and their future today and tomorrow," Sisi said.
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.
Mubarak's successor, Morsi, lasted one year in office, winning Egypt's first democratic presidential poll only to quickly alienate many who held mass rallies demanding his resignation.
BA/BA