Voting will be extended into a second day on Tuesday after Egyptians overwhelmed polling stations' ability to cope in their first election since a popular revolt toppled Hosni Mubarak's 30-year rule in February.
About 50 million people out of a population in excess of 85 million are eligible to vote for candidates from 50 registered political parties.
Monday's peaceful turnout in what is the first round of a complex voting process confounded fears of violence after a week of riots in which 42 people were killed and more than 2000 wounded.
People lined up early in many places and some polling stations opened late due to administrative delays. Officials blamed a delay in some Cairo constituencies on late arrival of ballot papers and a shortage of ink and administrative officers.
The official opening time was 8am and voting hours were extended to 9pm on Monday.
The BBC reports there had been fears the vote might be delayed after protests against the interim military rulers who replaced Mr Mubarak. Protesters occupying Tahrir Square in the capital Cairo have boycotted the vote.
Protesters fear the Supreme Council of the Armed Forces led by Field Marshal Hussein Tantawi, which is overseeing the transition to democracy after decades of authoritarian rule, is trying to retain power.
Observers say the parliamentary election could loosen the army's grip on power and sweep long-banned Islamists into the legislature.
Political transformation in the most populous Arab country will reverberate across the Middle East, where a new generation demanding democratic change has also toppled or challenged the leaders of Tunisia, Libya, Syria and Yemen.
Complex voting process
Monday marked the first step of an election timetable which lasts until March 2012 and covers two houses of parliament.
The country's 27 provinces will initially vote in three separate rounds to elect a lower house of parliament, the People's Assembly, which has 508 members.
Voters in nine provinces, including Cairo, Port Said, Alexandria and Assiut are casting ballots on Monday and Tuesday. Other provinces take their turns through December and early January.
Voting for the upper house, or Shura Assembly, of parliament takes place after that.
Official results from the first phase of voting should be announced on Wednesday. The final results of the parliamentary elections are expected on 13 January.
A presidential election is supposed to be held by mid-2012.