A total of 6,639,385 people are eligible to vote, and fifty per cent plus one have to say "yes" to the question whether they want the conformation of the new constitution for it to be passed.
Apart from Serbia, voting is taking place in Kosovo's Serb-majority municipalities as well as in Serbia's embassies and consulates in 24 countries.
A total of 8,386 polling stations are open today and tomorrow from 7 am to 8 pm. The Election Commission has until 8 pm on November 2 to publish the referendum's official results.
Given that there is no electoral blackout, Serbian President Boris Tadic said after voting that the new constitution was "a discontinuity with (former President Slobodan) Milosevic's times... This vote is very important. We have to adopt the highest legal act and distance ourselves from the times which were not Serbia's finest hour".
Prime Minister Vojislav Kostunica said the new constitution rounded off Serbia's statehood and brought it into a significant, more peaceful, more stable and more serene time.
"All those who today and tomorrow are taking part in the referendum are not just participants, but also creators of Serbia's new beginning and age," he said after voting.