Long queues are reported nationwide as Kenyans vote in an election that observers describe as the most important in the country's history.
Voters are complaining of having to wait under a hot sun for several hours.
There has been a series of violent incidents around the port town of Mombasa, with at least five police officers killed in one attack.
Authorities have urged Kenyans to avoid the widespread bloodshed that followed the disputed 2007 election.
More than 1,000 people died in ethnic and political violence following claims the poll had been rigged.
One of the frontrunners in the presidential poll, Uhuru Kenyatta, is due to face trial at the International Criminal Court (ICC) next month in connection with the 2007 violence - he denies organising attacks.
His main rival is Prime Minister Raila Odinga, who says he was cheated of victory last time.
Reports from around the country suggested long queues of voters had formed even before polling stations opened - and some voters, such as those in Eldoret, are waiting up to 10 hours to cast their ballots.
Some technical difficulties were reported with newly instituted biometric voting kits - designed to counter claims of vote-rigging and long delays in announcing poll results that were partly blamed for the violence in 2007.
In places, electoral officials are having to use the manual voter registers, delaying voting. But Lilian Mahiri-Zaja, vice-chair of Kenya's independent electoral commission, said the registers were complete and there was no reason why the election should not be credible.
Five police officers and at least six other people - including several attackers - died in the assault in the early hours in Changamwe, half an hour's drive inland from the centre of Mombasa.
There have been further disturbances in the town of Kilifi, north of Mombasa, where six civilians were killed, but details of the incident remain sketchy.
Police pointed the finger at Kenya's coastal separatist group, the Mombasa Republican Council (MRC), but it denied responsibility, saying the group only sought change through peaceful means.
Waiting in line outside polling stations in Nairobi hours before polls opened, the atmosphere was calm and people chanted "peace", reports the BBC's Gabriel Gatehouse.
In Garissa, frustration grew in the long queues as the heat beat down, our correspondent reports. Some used umbrellas to shelter from the sun and others bought water to pour over their heads.
Kenyans will choose a president, members of parliament and senators, county governors and members of 47 county assemblies.
However, our correspondent in the capital says all eyes are on the presidency.
Eight candidates are standing but it is essentially a two-horse race pitting Mr Odinga against Mr Kenyatta, he says.
The polling stations are open from 06:00 to 17:00 local time (03:00-14:00 GMT), though officials say some may have to stay open until late into the night to allow everyone to vote.
Presidential candidates must secure support from across the country to be declared the winner, so they cannot just rely on support from their ethnic groups, as has been the case in previous elections.
Official results will be announced by 11 March by the electoral commission.
Source: BBC News