Many supporters waited for hours in searing heat to glimpse the 66-year-old Nobel laureate, who is running for political office for the first time in the by-elections, after being locked up by the junta for most of the past 22 years.
The 45 seats at stake are not enough to threaten the ruling party's majority, but a seat in parliament would give the National League for Democracy (NLD) leader a chance to shape legislation for the first time.
Observers believe Myanmar's new quasi-civilian government wants Suu Kyi to win a place in parliament to burnish its reform credentials and smooth the way for an easing of Western sanctions.
The polls were however marred somewhat by allegations of ballot-paper irregularities, notably that wax had been put over the check box for the NLD that could be rubbed off later to cancel the vote.
“This is happening around the country,” NLD spokesman Nyan Win told AFP. “I have sent a complaint letter to the union election commission. If it continues like this it can harm the prestige of the election.”
In the run-up to the vote, the party decried alleged intimidation of candidates and other irregularities. Suu Kyi said on Friday that the vote could not be considered “a genuinely free and fair election” but stopped short of announcing a boycott.
A 2010 general election, won by the military's political proxies, was plagued by complaints of cheating and the exclusion of Suu Kyi, who was released from seven straight years of house arrest shortly afterwards.
The seats being contested today were made vacant by MPs who joined the government.
Polling was to close at 0930 GMT and official results are expected within a week, although the parties may declare how they fared earlier.
In rural villages dotted between parched fields, people stood in front of their thatched bamboo homes and waved enthusiastically as Suu Kyi's convoy snaked past today, whipping up thick clouds of dust.
A crowd of supporters and journalists mobbed the activist as she visited a polling station in the rural constituency of Kawhmu, where her main rival is a former military doctor with the ruling Union Solidarity and Development Party.
Voters, many in traditional ethnic Karen dress, queued patiently in the heat to cast their votes. In stark contrast to life under the junta, many openly expressed their support and affection for “The Lady”.
“There's only been one person for us for 20 years,” said Tin Zaw Win.
“We believe in her and want to vote for her. Almost my whole village will vote for Aunt Suu,” he added. Some people complained that their names were missing from the voter lists, although it was unclear how many were affected.
“I want to vote for Mother Suu but they haven't given me my ballot paper so I'm here to demand it,” Zin Min Soe told AFP at a polling station in Kawmhu.
“They can't just lose my vote,” he added.
The NLD swept to a landslide election victory in 1990, but the generals who ruled the country formerly known as Burma for decades until last year never recognised the result. Suu Kyi was under house arrest at the time.