Vieira, who ruled Guinea-Bissau for 23 years, was killed by members of the army on March 2, apparently in revenge for a bomb attack that claimed the life of the army chief, General Batista Tagme Na Waie.
Earlier this month, presidential candidate and former minister Baciro Dabo was killed by the army in what they said was an operation to foil a coup plot. Another candidate pulled out of the race, saying he feared for his life.
Of those who remain, the leading contenders are three former heads of state.
Malam Bacai Sanha served as interim president from June 1999 to May 2000 and is the candidate for the long-dominant African Party for the Independence of Guinea and Cape Verde (PAIGC).
The PAIGC already controls 67 of the 100 seats in the country's national assembly.
Also running is Kumba Yala (2000-2003). His time in office was marked by wide fiscal mismanagement and sweeping arrests of opposition figures until he was brought down in a coup.
And another former head of state, running as an independent, is Henrique Rosa (2003-2005).
If no candidate wins an overall majority in the first round, the election will go to a run-off between the two highest placed contenders on July 28.
Whoever does win the vote will have to contend not just with the country's poverty, but with the corrupting influence of drugs trafficking.
One of Africa's poorest countries, it is a transit point in the cocaine trade to Europe from Latin America, according to the UN.
Raimundo Pereira, the country's caretaker president, described the poll as "an important step towards stability" and called for a high turn-out.
"I would liked to call on all of Guinea-Bissau's citizens to vote because this election is very important for the normalisation of the country," he told reporters after having cast his own vote.
In the Bario Militaro district, on the road to the airport, people cast their vote at an open-air polling station: a table had been set up on a veranda. Voters waited their turn on wooden benches in the shade of a mango tree.
"I'm voting and I hope there will be no more war," Oumar Soumare, a baker, told AFP.
In the Septembre district, in the heart of the capital Bissau, where voting had moved inside after the rain started, one civil servant told AFP: We haven't received our salaries for several months."
Around 600,000 of the country's 1.3 million population are eligible to vote.
Some 150 observers have been deployed to supervise voting and around 3,600 police, gendarmes and soldiers were on duty to ensure security.
But observers have been sceptical that the country was ready for a vote after the recent surge in violence.
For African human rights organisation Raddho, based in neighbouring Senegal, "the present atmosphere of fear and terror is not a favourable one for the organisation of credible elections."
In a bid to ensure the operation runs smoothly, regional west African bloc ECOWAS announced that it had paid the country's armed forces three months back-pay they were owed.
But other government employees are still waiting for their salary after three months without pay.
Guinea-Bissau is ranked 175 out of 177 countries in the 2007-2008 human development report by the United Nations Development Programme.
The 5.1 million euro (7.1 million dollar) elections have been entirely funded by foreign donors.
The former Portuguese colony, which won its independence in 1974, has been overwhelmed and weakened by the international drugs trade, which observers say has raised the stakes in the power struggle between the army and politicians.
Some 2,700 polling stations nationwide began opening at 7:00 am (0700 GMT), with the polls due to close at 5:00 pm.
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