Counting starts after closing, with early results expected soon after.
The vote is widely expected to propel Jacob Zuma, the leader of the ruling African National Congress (ANC), to the presidency.
Mandy Weiner, a journalist based in South Africa, speaking to Al Jazeera at 11pm local time (21:00GMT), said that voting was still taking place at many polling stations.
"There are still voters standing in queues waiting to cast their ballots," she said.
"The reason for this is that there has been a serious problem with a shortage of ballot papers and ballot boxes."
Al Jazeera's Jane Dutton, reporting earlier from a polling station in Johannesburg, said that officials had resorted to using egg crates after they ran out of ballot boxes.
Election turnout was expected to top 80 per cent - the highest number of voters since South Africa's first multiracial election in 1994.
David Monyae, a political analyst in Soweto, told Al Jazeera: "It appears we are entering a post-liberation era in the country. We all know the ANC is going to win, but the question is, 'when?' and 'with what percentage?'
"We are not sure if the Democratic Alliance is going to remain as the main opposition party. A lot of changes are taking place."
Opinion polls have tipped the ANC to win at least 60 per cent of the vote, with the new Congress of the People (Cope) and the Democratic Alliance (DA) expected to take about 10 per cent each.
But Helen Zille, leader of the DA, who voted at a polling station in Cape Town, said she was hopeful of a good result.
"I think South African voters know what we need to do to save democracy," she said.
Haru Mutasa, Al Jazeera's correspondent in Cape Town, reported that many people there were voicing support for opposition parties.
"People are saying they have become disillusioned with the ANC, and that they have taken too long to deliver on their promises. Too many people still live in poverty, they want houses, water and education.
|Desmond Tutu, South Africa's famed archbishop, voted in Cape Town [Reuters]
"It is likely the vote here [in the Western Cape] will go to the Democratic Alliance."
But Zuma's promises to clean up government and improve public services have struck a chord among many South Africans, and his embrace of traditional culture has proved popular.
The ANC leader had corruption charges against him dropped two weeks ago, but the scandal has done little to dent the popularity of his party, still revered for leading the fight against apartheid.
Voting in his home province of Kwazulu-Natal, Zuma said: "When I grew up, I did know that this day would come. This makes me feel great and it's a feeling far different from the one that we had under the apartheid government."