Although the outcome of the poll will not be clear for at least 36 hours, a densely packed crowd blocked a busy road beside the headquarters of Suu Kyis National League for Democracy in Yangon as they cheered and waved red flags.
The NLD is expected to win the largest share of votes cast by an electorate of about 30 million, who chose from thousands of candidates standing for parliament and regional assemblies, Reuters reported.
But a legacy of rule by military junta means Suu Kyi, who led the campaign for democracy, cannot become president herself. And whatever the result, Myanmar is heading into a period of uncertainty over how she and other ascendant parties negotiate sharing power with the still-dominant military.
A pariah state until a few years ago, Myanmar has had little experience organising elections. Some 10,000 observers were enlisted to scrutinise the process. Early indications from the monitors were that voting was mostly trouble-free, with only isolated irregularities.
"From the dozens of people we have spoken to since 6 a.m. today, everybody feels they have been able to vote for whoever they wanted to in security and safety," said Durudee Sirichanya, one of the international observers.
In the city of Mandalay, about 100 people were stopped from voting after officials discovered they were outsiders who had been mysteriously added to the register and then bussed to the polling station.
A Referendum on Reform
The main concern about the elections fairness arose before the election. Activists estimated that up to 4 million people, mostly citizens working abroad, would not be able to vote.
Religious tension, fanned by Buddhist nationalists whose actions have intimidated Myanmars Muslim minority, also marred the election campaign. Among those excluded from voting were around a million Rohingya Muslims who are effectively stateless in their own land.
Still, there was excitement among voters about the first general election since a quasi-civilian government replaced military rule in 2011, which was widely seen as a referendum on the countrys unsteady reform process.
"Ive done my bit for change, for the emergence of democracy," said Daw Myint, a 55-year-old former teacher, after she cast her vote for the NLD in Yangon.
Suu Kyis car inched through a scrum of news photographers outside the polling station in Yangon where the 70-year-old Nobel peace laureate came to vote.
She was stony-faced as bodyguards shouted at people to move aside, but a jubilant cry of "Victory! Victory!" went up from the crowd of well-wishers as she went inside.
Many voters doubted the military would accept the outcome of the vote if the NLD wins.
But in the capital, Naypyitaw, military Commander-in-Chief Min Aung Hlaing said there would be no repeat of the last free vote in 1990, when Suu Kyi won but the army ignored the result. She spent most of the next 20 years under house arrest before her release in 2010.
"If the people choose them (the NLD), there is no reason we would not accept it," the senior general told reporters.
"Very Silly" Constitution
Results from the election are expected to come in slowly, with a clear overall picture not likely to emerge until Tuesday morning.
Suu Kyi is barred from taking the presidency herself by provisions of a constitution written by the junta to preserve its power.
But if she wins a majority and is able to form Myanmars first democratically elected government since the early 1960s, Suu Kyi says she will be the power behind the new president regardless of a constitution she has derided as "very silly".
Suu Kyi started the contest with a sizeable handicap: even if the vote is deemed free and fair, one-quarter of parliaments seats will still be held by unelected military officers.
To form a government and choose its own president, the NLD on its own or with allies must win more than two-thirds of all seats up for grabs. The ruling Union Solidarity and Development Party would need far fewer seats if it secured the backing of the military bloc in parliament.
However, many voters were expected to spurn the USDP, created by the former junta and led by former military officers, because it is linked with the brutal dictatorship that installed President Thein Seins nominally civilian government in 2011.
An inconclusive result could thrust some of the 91 parties contesting the election, including many representing Myanmars myriad ethnic minorities, into a king-maker role.
Even if the NLD is victorious, the military will retain significant power. It is guaranteed key ministerial positions, the constitution gives it the right to take over the government under certain circumstances, and it also has a grip on the economy through holding companies.
(Additional reporting by Aung Hla Tun, Andrew Marshall, Aubrey Belford, Simon Webb and Timothy McLaughlin; Writing by John Chalmers; Editing by Larry King)