The voters are choosing their first president since last year's ouster of longtime ruler Hosni Mubarak. The 13 candidates in the running include Islamists, liberals and two with military backgrounds.
No outright winner is expected from the two-day vote, so a runoff is scheduled for mid-June, with the winner expected to be announced on June 21. Around 50 million people are eligible to vote.
The winner will face a monumental task. The economy has been sliding as the key tourism industry dried up - though it starting to inch back up. Crime has increased. Labor strikes have proliferated.
For most of his 29-year rule, Mubarak - like his predecessors - ran unopposed in yes-or-no referendums. Rampant fraud guaranteed ruling party victories in parliamentary elections.
The Associated Press contributed to this report.