Myanmar, also known as Burma, is voting in the first openly contested general elections in 25 years after decades of military rule.
The ruling Union Solidarity Development Party (USDP), backed by the military, is one of the frontrunners.
Aung San Suu Kyi’s National League for Democracy (NLD) is expected to make large gains, although she is barred from running for the presidency.
Large crowds gathered in Yangon as Aung San Suu Kyi arrived to cast her vote.
Across the country, long queues formed at some polling booths, with reports of people queuing from long before dawn.
About 30 million people are eligible to vote in the election in Myanmar.
Clear results are not expected until November 9.
More than 6,000 candidates from over 90 parties are vying to be elected to the 664-seat parliament in the first national elections since a nominally civilian government took power in 2011.
However, 25% of seats are reserved for unelected military representatives, who are expected to side with the USDP.
Aung San Suu Kyi, a former Nobel Peace Prize laureate, is barred from the presidency as the constitution disqualifies anyone with foreign offspring.
On November 5, Aung San Suu Kyi said she would be “above the president” if her party won. The NLD must take 67% of all contested seats in order to gain a majority.
Current President Thein Sein said he would accept the election result.
Hundreds of thousands of people – including minority Rohingya Muslims – have been denied voting rights, raising concerns about the fairness of the poll.
Ahead of the vote, security has been stepped up across the country, with some 40,000 police guarding polling stations.
Ruled by the junta for nearly half a century, Myanmar has seen economic and political reform in recent years.
Aung San Suu Kyi has already raised concerns about poll fraud and voting irregularities. In the 1990 election, the NLD won a majority, but the results were largely ignored by the generals.
For its part, the government has warned that rapid change could lead to civil unrest.