Human rights organizations and anti-government groups have bitterly accused the government of neglecting cyclone victims to advance its political agenda, and have criticized its proposed constitution as designed to perpetuate military rule.
Local journalists said they saw cases of intimidation of voters at various polling stations around the country.
State TV on Saturday broadcast a video of two women singing a pop-style song with the lyrics: "Let's go vote ... with sincere thoughts for happy days."
In a country where the last election was held 18 years ago, many people had no idea how to vote. Some asked each other or officials, "Where do I go?" or "What do I do?" as they walked into curtained booths to cast their ballots.
The referendum seeks public approval of a new constitution, which the generals say will be followed in 2010 by a general election. Both votes are elements of what the junta calls its "roadmap to democracy."
But the proposed constitution guarantees 25 percent of parliamentary seats to the military and allows the president to hand over all power to the military in a state of emergency - elements critics say defy the junta's professed commitment to democracy.
It also would bar Nobel Peace Prize laureate Aung San Suu Kyi, the detained leader of the country's pro-democracy movement, from public office. The military refused to honor the results of the 1990 general election won by her National League for Democracy party.
Some 27 million of the country's 57 million people were eligible to vote, although balloting was delayed for two weeks in the areas hardest hit by the May 3 cyclone. Final official results of the referendum will not be announced until after late voting on May 24 in areas badly hit by recent Cyclone Nargis.
State media say 23,335 people died and 37,019 are missing from Cyclone Nargis, and international aid organizations say the death toll could climb to more than 100,000.
The fear of the military, which has ruled since 1962, is so great that few people among those who voted were expected to have marked "X" - which stands for "No" to the constitution - on their ballot, making the outcome a foregone conclusion.
A voting official who supervised two booths at a town in the country's Irrawaddy Delta region - some parts of which still voted despite the devastation wrought by the cyclone - said the vote in favor was 83 percent and 95 percent, respectively. He asked not to be further identified for fear of getting into trouble.
The editor of a respected Myanmar newsmagazine who had reporters stationed around the country said the information he received showed the vote was not completely free and fair.
"The essence of secrecy is totally lost in some of the polling booths," said the editor, who also spoke on condition of anonymity for fear of reprisals.
He said irregular practices seen by his reporters included officials telling voters, "Don't forget to put the tick, the right mark," as they got ready to cast their ballots.
Voting officials also would sometimes pull aside the curtains protecting the privacy of the voting booths, in addition to asking voters to affix their fingerprints on the ballot papers. Other journalists witnessed voters clutching three or four national registration cards, which they exchanged for an equal number of ballots, a violation of voting rules.
Altsean Burma, a regional human rights group, said authorities instructed village officials to cast "Yes" votes on behalf of people who did not turn up at polling stations by 1 p.m.
Aye Aye Mar, a 36-year-old homemaker, looked frightened when asked if she thought anyone would vote "No."
Her eyes darted around to see if anyone was watching, and then she whispered, "One vote of 'No' will not make a difference." Then she raised her voice. "I'm saying 'Yes' to the constitution."
Min Lwin, 40, made it clear that he did not believe his vote counted.
"What choice do I have?" he said, before quickly walking away.
Polling stations closed at 4 p.m., but a final count was not expected for two weeks. It is not clear when the results will be out.
Balloting took place across most of the country but was put off until May 24 in the areas most stricken by Cyclone Nargis a week ago - including the biggest city, Yangon. The U.N. estimates that 1.5 million to 2 million people have been severely affected.
The junta has so far allowed in only material assistance and has rejected the large-scale presence of foreign relief workers who have capabilities that Myanmar lacks to cope with the disaster.
"Even as hundreds of thousands of its citizens struggle for basic shelter, food and health care, Myanmar's government has prioritized acceptance of the new constitution," Amnesty International said.
It said the proposed constitution was "an effort to undermine respect for human rights and to entrench military rule and impunity."
Groups that led last year's pro-democracy demonstrations also issued protests while carrying on with their campaign urging people to vote "no."
In nearby Malaysia, about 500 Myanmar activists demonstrated Saturday outside their country's embassy in Kuala Lumpur, demanding that the junta call off the referendum even after voting began.
The AP's Ed Donahue reports the slow pace of getting relief supplies to cyclone victims isn't stopping donors from giving.
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