But there are no normal circumstances in a country where the constitution guarantees a bloc of seats to the military, Suu Kyi is barred from the presidency and an alliance of radical monks and nationalists launched a last-ditch campaign to thwart her.
The last time her National League for Democracy contested national elections, Suu Kyi was detained for what became 15 years of house arrest.
The NLD still won that 1990 vote by a landslide, but the ruling junta simply refused to accept the result and threw hundreds of the NLD's supporters and newly-elected MPs in jail. Many died from torture and illness.
Suu Kyi was in assertive mood as she delivered her final message before the election. For more than an hour, she answered questions about an election that represents the next chapter in a life inextricably enmeshed with the turbulent history of her homeland.
Some 30 million voters were eligible to cast ballots.
Queues built up before daybreak at polling stations across the country in a sign of the enthusiasm that has accompanied the vote. There are no opinion polls, but she has drawn huge and fervent crowds as she has campaigned and there is little doubt about the popularity of the NLD.
But in the tea-houses and restaurants, there was a growing sense of foreboding among NLD supporters.
They feared another victory could be blocked by a mixture of dirty tricks, voter list irregularities, bribes, intimidation, as well as a last-ditch intervention by radical Buddhist monks drawing on anti-Muslim nationalism.
"I fear that they will do everything to swing the vote," said Kyaw Mya, 78, a father of six and former motorbike mechanic, referring by "they" to a combination of the military, ruling party and Buddhist nationalists.
"If the NLD loses, its supporters will cry foul and rise up. But if the NLD wins, the military will not want Mother Suu to run the Government. There will be trouble."
Thousands of election observers were deployed yesterday, but not every polling station could be monitored and in rural areas, many voters worry about the security of their ballot. "We haven't had any complaints so far," Win Naing, an election commission official, told AFP yesterday.
Suu Kyi sounded her own concerns, noting violations of electoral law by her opponents. She expressed fear about the "extent to which the authorities are prepared to go to win the election".
These are the first elections since the generals partially stepped back from power to end five decades of military dictatorship. Since 2011, Burma has been ruled by Thein Sein, a former general, and other ex-senior officers. But this is far from the full transition to democracy that was initially hailed by some Western leaders.
Under the 2008 constitution, the commander-in-chief of the armed forces will appoint the ministers of the interior, defence and border affairs. He will also name military officers to occupy 25 per cent of seats in the new Parliament. That bloc will be able to veto any change to the constitution that enshrines military influence.
It means the NLD must win two-thirds of the seats to be able to force through change. With many ethnic parties likely to do well in their areas, weeks of post-election horse-trading could be on the cards.
Suu Kyi's foes have been trying to undermine her chances with a series of ruses. Voters in several constituencies said they had been offered inducements such as money, food parcels or free transport to rallies. Voter lists are strewn with inaccuracies.
The military forces - a million voters when families are included - have been told by their officers to support a candidate who will protect "race and religion" and is free of "foreign influences". Telegraph Group Ltd, AFP, AP
