Ballot boxes are transparent but the MDC says the vote is not
A local poll monitor told the BBC that the voting process had been "smooth", but pointed to earlier problems.
By the afternoon, long queues of voters had disappeared from many areas.
As he cast his ballot, President Robert Mugabe dismissed as "nonsense" claims that the poll would be rigged and said he was confident of victory.
No doubt
Human rights groups say the poll cannot be free and fair and suggest that thousands of dead people are listed on the electoral roll.
Reginald Matchaba-Hove of the Zimbabwe Election Support Network, which has some 6,000 observers in the 8,000 polling stations, told the BBC's Focus on Africa programme that the atmosphere had changed in the past few weeks, when foreign observers started arriving.
We have been ruled by the same party for the past 25 years and they have done nothing to help us in our cause.
Velempini, MDC supporter Zanu-PF is the only party in Zimbabwe that has a vision for the country.
Olley, film maker and government supporter
Voters' views Have Your Say
On Thursday, Zimbabwe arrested two British journalists working for the Sunday Telegraph on charges of reporting on the country's election without state accreditation, police said.
The offence carries a fine and up to two years in prison.
Toby John Harden, 37, and Julian Paul Simmonds, 46, were arrested while travelling with an opposition politician.
Counting is due to start now that the polls have closed. Preliminary results are expected within 48 hours.
Mr Mugabe was confident as he turned up to vote in the capital, Harare, accompanied by his wife Grace and young son Chatunga.
"It's going to be a victory for us - by how much, well, that is what we will see."
As he cast his vote in Harare, opposition Movement for Democratic Change leader Morgan Tsvangirai also said he was confident of victory, although he said the poll was not free and fair.
"The people will speak today and I am hoping that the outcome will be an MDC victory, I have no doubts about that," he said.
One hundred and twenty parliamentary seats are up for grabs. A further 30 MPs are appointed by President Mugabe.
A two-thirds majority for the ruling Zanu-PF party would allow the constitution to be changed, which correspondents say could be crucial when it comes to planning for the post-Mugabe era.
'Ghost voters'
Although the campaign has been relatively peaceful, the MDC says the election has been skewed in advance towards Zanu-PF for a number of reasons:
State-controlled radio and television, which have a monopoly, favour Zanu-PF;
Until recently, they were often refused permission to hold rallies and their activists harassed;
Food aid has been denied to opposition supporters, they say;
Constituency boundaries have been changed to favour the ruling party.
The government dismisses all such reports as groundless, and has introduced transparent ballot boxes it says will reduce the scope for cheating.
Despite the general atmosphere of peace, an MDC polling agent in the south-western Insiza constituency has been abducted, the party says.
Critics say the land seizures ruined the farming industry and triggered food shortages, inflation and unemployment.
The president says the economic crisis is the result of efforts by Washington and Europe, led by former colonial power Britain, to unseat him.
A small selection of foreign election monitors have been invited. Many of those critical in the past have been excluded.
President Mugabe, 81, has led his party's campaign, although he has said he will not seek re-election in the 2008 presidential election.
The main opposition — the , claims that the election has been rigged.
Elections in Zimbabwe began with both the ruling and opposition parties predicting victory.

Current president Robert Mugabe predicts a "mountainous victory" for his party, the  (Zanu-PF). The main opposition —  (MDC) claims the election is being rigged, and despite being allowed to freely campaign, the government's intimidation of voters and moves to hurt opposition supporters will prevent the MDC win. 

The government recently withheld food aid from those supporting the MDC, according to a United Nations report. The UN further reports the government dismissed election officials and poll workers suspected of supporting MDC.

Criticism of the government has been loud. Last week, a Catholic archbishop in Zimbabwe urged followers to start a non-violent, popular uprising against Mugabe, and rallies have been common in recent days. The previous elections, which the MDC almost won, were marred by violence and similar allegations of vote-rigging.

More than 5.7 million Zimbabweans are registered to vote, and can cast their ballots at one of the more than 8,000 polling stations.