Police were stationed outside Cairo polling stations, with the state-run Middle East News Agency (Mena) saying the interior ministry had set up "a tight security plan... to guard the polling stations from the outside".
The election takes place against a backdrop of protests over rising food prices and poor wages, which lasted for two days.
Police fired tear gas and shot skyward as about 7,000 protesters hurled stones toward them in the Nile Delta city of Mahalla el-Kobra on Monday.
Since protests began, about 300 people have been arrested, 90 injured and one teenage boy was killed after a rubber bullet hit him at close range, according to Amr el-Kahky, Al Jazeera's correspondent in Egypt.
Some workers and residents were arrested after they destroyed a large portrait of President Mubarak as well as banners of his National Democratic party (NDP).
"There is a combined frustration at the government's failure to find resources to lower high prices and anger towards municipal council corruption," el-Kahky reported.
Mubarak has lifted import duties on some food items in an effort to soften economic hardship brought on by a near doubling of prices of foodstuffs due to international and local market pressures.
Despite this, nearly 40 per cent of the country lives below or near the poverty line of $2 a day.
Mustafa Fouda, the leader of workers from the Mahalla textile factory, 110km north of Cairo, said on Tuesday: "The situation is calm but tense.
"The clashes could start again around 5 o'clock when the workers finish their shift and students finish class."
Momentum has been gathering for another planned strike on May 4.
A message on the Facebook social networking site, where 64,000 people joined the group calling for action, said: "We succeeded on April 6, so let's do it again on May 4."
The NDP is fielding a candidate for every one of the 52,000 council seats up for grabs, with polls set to close at 7pm (1700 GMT).
Mohammed Abdel Meguid, 28, said from a Cairo polling station: "I've come to vote in the hope of having a life that is less hard, with no bread problems.
"We hope that these elections will change things a bit, if they're not rigged like the others when the NDP has always won."
|The poll takes place with a backdrop of protests|
over rising food prices and poor wages [EPA]
These local elections have an unprecedented importance following a 2005 constitutional amendment requiring presidential candidates to secure the backing of councillors.
Parties with presidential ambitions, including the banned opposition Muslim Brotherhood whose members sit in parliament as independents, now need the support of at least 10 members of every local council in at least 14 provinces to stand.
The next presidential election is set for 2011, with many expecting the veteran 79-year-old Mubarak to stand down in favour of his son, Gamal Mubarak, a senior NDP member.
The Brotherhood had been due to field 21 candidates out of about 4,000 the group originally put forward after a wide-ranging government crackdown left many would-be candidates behind bars or blocked from registering.
In response, the Brotherhood announced a boycott and called on
all Egyptians to follow suit.
Hussein Ibrahim, deputy head of the Brotherhood's bloc in parliament, said on Monday that authorities had used "illegal and immoral means" to exclude Brotherhood candidates, including "the arrest of 1,000
members, administrative obstacles to candidates registering and using prisoners as hostages".
Mohammed Mahdi Akef, the Brotherhood's supreme leader, said on Monday: "We will continue to fight politically and legally to invalidate the municipal elections if they are held."
Municipal polls were postponed for two years in 2006 in what observers said was a way to avoid another success for the Brotherhood.