The government has praised the draft for its consolidation of democracy and rule of law in this country that seeks to join the European Union.
The document also declares the province of Kosovo -- whose majority ethnic Albanian population wants independence -- to be an integral part of Serbia. The province has been administered by the United Nations since 1999.
Mainstream parties have asked their supporters to vote, with ultranationalists stressing Kosovo's fate and centrists highlighting better safeguards on human rights and "European values."
Some liberal parties are boycotting because they see the new constitution as vague and more nationalistic.
Voters are being asked to simply vote "yes" or "no" to the proposed constitution, which would replace the 1990 version passed when former Serbian and Yugoslav President Slobodan Milosevic was in power.
'Serbia And Its People'Casting his ballot today, one pensioner said the new constitution represented a new beginning for the country, and that it "will bring great changes in the sense of a new life for Serbia and its people."
Of course, what is meant by "Serbia and its people" is not entirely clear as voters in Serbia head to some of the more than 8,000 polling stations.
Though the proposed constitution specifically lays claim to Kosovo as part of Serbia, even officials in Belgrade have conceded that the document cannot be enforced if the ethnic Albanians that make up over 90 percent of Kosovo's population opt for independence. Though the roughly 100,000 ethnic Serbs still living in Kosovo are eligible to vote in the referendum on a new constitution, the 2 million Albanians living there are not, as they have not been included in voter lists after boycotting Serbian elections since 1990.
In keeping with Serbia's desire to join the European Union, another part of the new constitution says: "The Republic of Serbia is the state of the Serbian people and of all the citizens who live there. The state is based on adherence to European principles and values."
The decision of Montenegro, Serbia's last partner from the former Yugoslavia, in June to declare its independence necessitated that Serbia adopt a new constitution.
At least half of Serbia's 6.6 million eligible voters must cast their ballots in favor of the new constitution for it to pass. All the country's mainstream parties called on their supporters to vote in the referendum. Most polls conducted before the referendum indicated the electorate would vote in favor of it.
(compiled from agency reports)