From remote Aegean islands to the shadow of the 2,400- year-old Parthenon in Athens, Greeks despairing at years of austerity - and angry at capital controls this week that have closed banks and prompted a clean-out of supermarket shelves - cast their ballots.
Polls show opinion evenly divided between 'Yes' and 'No' with many believing neither result would provide a quick and clear solution to Greece's debt woes.
"When you have to choose between two bad solutions, you choose the least bad, and that's clearly 'Yes'," said Dimitris Kavouklis, 42, as he voted in an upmarket district of the capital.
But Dimitris Halatsis, a teacher, said on such a "crucial day" he was voting 'No' because "it's the only chance the government and Greece have to apply pressure" on its international creditors.
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Tsipras said he was confident of a 'No' as he voted in his northern Athens neighbourhood, saying that would force concessions from the creditors to give Greeks less austerity and more "dignity".
Tsipras's flamboyant finance minister, Yanis Varoufakis, has accused Athens's creditors of "terrorism" for raising the spectre of Grexit. He insists no legal mechanism exists to make it drop out of what is meant to be an "irreversible" monetary union.
Varoufakis has vowed to resign if a 'Yes' prevails, and the pressure would be on Tsipras to do the same.
Voting was to close at 7:00pm (2130 IST), with results expected a couple of hours later.
Michelis, an 80-year-old first through the doors of a primary school being used for the vote in central Athens, said he too was saying 'No' "because they (the creditors) will take us more seriously".
Theodora, 61, a retired journalist, said she was voting 'Yes' because "it's a 'Yes' to the European Union".
In the largely middle-class Pangrati neighbourhood, voter turnout was high, with even the very elderly making their way determinedly up a flight of 40 steps to reach polling booths.