The two-day election, expected to draw about 75 percent of Egypt's 53 million eligible voters Wednesday and Thursday, promised to end 15 months of military rule since the Feb. 11, 2011, ouster of Mubarak following 18 days of demonstrations.
Eleven candidates are on the ballot and more than 50 million people across Egypt's 27 governorates are eligible to vote.
The military's Supreme Council of the Armed Forces has ruled the country since Mubarak's ouster. In November, the generals -- facing huge bloody protests -- bowed to the popular will and promised to hand over power to an elected president by June 30.
Long lines were seen at voting places in Mansoura, where many voters said they were unsure which candidate they would choose, the Egypt Independent reported.
The uncertainty also was voiced in the Heliopolis neighborhood of Cairo where one woman told the Independent, "I guess I will go in and decide on the spot."
Candidate Amr Moussa, a former Arab League leader, waited about 90 minutes to cast his ballot in Cairo, calling the voting an important lesson in democracy.
"Egyptians should have good judgment in selecting the person who would shape Egypt's future over the next period," Moussa said. "We are up to the challenge."
Al-Masry al-Youm reported People's Assembly Speaker and Muslim Brotherhood leader Saad al-Katatny told reporters while waiting to vote the winner -- whether himself or another candidate -- would reflect the will of the people and should be respected.
In Shubra, voters waited to cast ballots at one polling station against a backdrop of military troops, military police and civilian police, the Independent said.
"It's an important day -- the first time I'm voting because for once we don't know who will win. What I hope is that there is no problems by supporters of failed candidates and accept the result," voter Tarek Emad said, saying he would vote for Moussa. "The important thing is to come out of this current phase to safety."
Outside Cairo, voter turnout has been between low and moderate, officials said.
In a polling station in one of the villages near Sohag, the lack of phosphoric ink and ballot box locks forced judges to keep the station closed.
In Suez, one election judge said about half the people who were supposed help run the polls didn't arrive earlier in the day.
Local watchdog Activists without Borders said in a statement some of members reported supporters of the Muslim Brotherhood candidates have been trying to influence voters.
If the elections don't produce an outright winner, a runoff is scheduled June 16-17.