Aung San Suu Kyi's National League for Democracy (NLD) is expected to win the most seats, although she is barred from the presidency.
The ruling Union Solidarity Development Party (USDP), backed by the military, has been in power since 2011.
Large crowds gathered in Yangon as Ms 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.