More than 2,000 Thai soldiers in dress uniform are pulling an elaborately decorated chariot carrying the princess's remains through Bangkok.
The body of the princess, who died 10 months ago aged 84, will be cremated on a 40m (130ft) high funeral pyre.
Correspondents say the $10m (£6.7m) funeral is intended to reinforce the monarchy's status in Thai society.
It is taking place at a time of intense political turmoil, in part fuelled by uncertainty over the succession of King Bhumibol Adulyadej, they add.
Anti-government protesters from the People's Alliance for Democracy (PAD) have also been occupying the main government offices for more than two months, with the aim of toppling the administration led by Prime Minister Somchai Wongsawat.
They claim Mr Somchai is a proxy for former PM Thaksin Shinawatra, who was ousted in a military coup in 2006.
Golden carriage
Thousands of Thais dressed in black lined the streets of central on Saturday morning to pay respects to Princess Galyani, whose remains were carried in an urn on top of an elaborately decorated 14-ton golden carriage, flanked by hundreds of soldiers and musicians.
Crown Prince Vajiralongkorn, representing the king, and Mr Wongsawat also took part in the procession, both dressed in white ceremonial dress.
The temporary royal crematorium, a complex of pavilions constructed on the Sanam Luang parade ground over seven months at a cost of $5.7m (£3.8m), has been lavishly decorated with flowers, garlands and carved banana stalks.
Members of the royal family will later perform the cremation ceremony, accompanied by guards from the three branches of the armed forces and court musicians.
Many other people are expected to perform religious rites and in the princess's honour at temples around the country.
According to the Royal Household, at least 1.5 million people have already paid their respects her remains, which have lain in state since her death.
The cremation on Saturday afternoon comes on the second day of the six-day funeral ceremony, which officially started on Friday with Buddhist monks chanting prayers, and the king lighting candles and incense at the Grand Palace.
Succession doubts
The BBC's Jonathan Head in the capital says the outward public affection for Princess Galyani is genuine - during her life she devoted herself to a range of charitable and artistic causes.
But this elaborate funeral is also intended to reinforce the monarchy's status at the apex of Thai society, at a time when its future role seems less certain, our correspondent says.
All eyes will be on King Bhumibol, who has been almost entirely out of public view this year and, at 80 years old, whose health is frail, he adds.
Our correspondent says that under Thailand's lese majeste laws the succession cannot be discussed, but it is still unclear what will happen after a reign that has already run for 62 years.
There are many doubts, which cannot be expressed, over the capabilities of the crown prince, the presumed heir to the throne, he says.
The difficulty of maintaining the official line that the monarchy is above politics was illustrated only last month, he adds, when Queen Sirikit presided over the funeral of a PAD protestor, giving the impression that she was taking sides.
BBC
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