Queues started building up at polling station in the capital, Nairobi, on Monday night.
The BBC’s Anne Soy says one queue stretched well over 200m by early Tuesday. The people at the front said they arrived before 21:00 on Monday.
Margaret Mwangi, 59, a fruit hawker, decided not to go home for the night. She camped at the station waiting to vote.
She’s second in the queue and hopes to go home after voting to follow the news on television.
The police are urging Kenyans to leave polling stations after casting their votes and wait for the results at home so as to maintain order and peace.
“In today’s poll, after you have made your decision known at the ballot, we ask that you support our security efforts by waiting for the poll results at the comfort of your homes,” the National Police Service says in a statement.
“We all want to live in an orderly society that respects the rule of law and one that is considerate to the wellbeing of its people,” it adds.
The police are providing security for the polling exercise across the country, with officers dedicated to each of the more than 46,000 polling stations.
During campaigns some politicians had urged supporters to remain at polling stations on voting day in order to “guard their votes”.
There are four candidates vying for the top job:
- David Mwaure – Agano Party of Kenya – the trained lawyer and preacher announced a run for the presidency in 2013 but later shelved his ambition
- Raila Odinga – Azimio la Umoja coalition – the former prime minister and veteran politician is making his fifth attempt to become president
- William Ruto – United Democratic Alliance – this is the first run for the presidency for the current deputy president
- George Wajackoya – Roots Party of Kenya – the lawyer and educationalist is making his first bid for the presidency