Until voting day for the referendum, the two sides have been out campaigning in force. Clashes over the past three weeks between Egyptian President Mohammed Morsi's supporters and opponents have left at least 10 people dead and about 1,000 wounded.
Supporters of Morsi of the Muslim Brotherhood want a yes vote on the new constitution, but opposition groups say it leans too heavily toward the imposition of Islamic law.
Opponents object to what they say is the document's vague language that could trample on human rights, where it says civilians will not be tried in military courts except in cases where the "crimes are susceptible to harm the armed forces."
Those on the yes side say the document will help end the political instability that has gripped Egypt since autocratic leader Hosni Mubarak was overthrown in March 2011 following a popular uprising.
Egyptians in Cairo and other urban areasvoted Saturday, with another round of voting scheduled next Saturday, Dec. 22.
Voting has been split over two days because there are not enough judges to monitor all the polling stations at the same time. Some members of the judiciary decided to boycott the process.
The shortage of judges was reflected in the chaos engulfing some polling stations, which led the election commissionto extend voting throughout the day, ultimately by four hours until 11 p.m. local time.
"I'm outside a polling station in Cairo. There's a long lineup outside the building of people trying to get in to cast ballots," CBC's Tom Parry said. "There is a mixture of opinions from people in line."
Egypt's army has temporarily been given police powers to help ensure security until the final results of the referendum are known.
About 120,000 soldiers will support 130,000 police officers who have been deployed to maintain order during the vote.
Official results will not be announced until after the second round of voting has ended, though observers expect unofficial results could leak out to suggest the vote trend.
If the draft constitution is voted down, a new assembly will have to be formed to draft a revised version, a process that could take up to nine months.