Health Secretary Humza Yousaf, Finance Secretary Kate Forbes and ex-minister Ash Regan are in the running to become Scotland’s next first minister.
Party members will be able to vote online from noon using the Single Transferable Vote system.
The result will be announced after the ballot closes on Monday 27 March.
Party members will be asked to rank the three candidates in order of preference, and if no single candidate secures more than 50% of votes on first preferences, the person in third place will be eliminated.
Ms Sturgeon, who announced her resignation last month, has indicated she would not be publicly backing any of the three candidates.
On Saturday Deputy First Minister John Swinney and SNP Westminster leader Stephen Flynn both endorsed Mr Yousaf.
However, polling expert Sir John Curtice, Professor of Politics at Strathclyde University said there was a “marked contrast” between the preferences of the public and SNP leadership.
He told BBC Radio’s Good Morning Scotland: “Nearly all polling has been of the public and SNP voters, rather than SNP members.
“If this election was being decided by the general public in Scotland, it seems pretty clear Kate Forbes would win.
“For clues as to what SNP members might think, we have been looking at the views of those who have voted for the SNP recently, or would vote for the SNP now.
“All of that polling points to SNP supporters being pretty much evenly divided between Humza Yousaf and Kate Forbes.”
The SNP membership once stood at more than 125,000, but that figure is believed to have declined.
The Mail on Sunday reported that the polling firm running the leadership ballot had received the names of 78,000 individuals from party headquarters.
On Sunday, Mr Yousaf told the BBC he would consider a snap Holyrood election and “any means necessary” so long as it was legal in order to secure independence.
Asked whether he would serve in a Kate Forbes cabinet if she was victorious, he said he would need assurances on policy.
Last week Ms Forbes criticised his record in government during the STV leadership debate.
She also said there was room for Mr Yousaf on her ministerial team before quipping “maybe not in health”.
The health secretary, who is campaigning in Stirling on Monday, is expected to pledge to stand up to any attempt to “trample over our democracy”.
He is expected to say: “Inclusivity, equality and respect for everyone were key pillars on which the Yes movement was built in the lead up to 2014.
“As a party, we cannot afford to have a leader who pulls us off that progressive path that will deliver us the independence for Scotland that we crave.
“It is so important that any SNP leader and first minister stands up to Westminster attacks and attempts to undermine Scotland’s Parliament and its democratic will.”
On Sunday Ms Forbes launched a “mini manifesto” for the leadership election which set out her stance on issues ranging from the economy, the NHS and tackling poverty.
Making a pitch to SNP members, she said: “We need a first minister who will lead us to independence, and it’s coming sooner than people think.
“I believe I’ve got what it takes to be the next first minister of Scotland, the first minister who will lead Scotland to independence.”
Ms Forbes came under fire early in the campaign after she revealed she would not have voted for same-sex marriage if she had been an MSP at the time, although she has also promised to uphold the rights of every Scot.
“We need a first minister who the people of Scotland can trust – a first minister who commands confidence,” she said.
“No-one can accuse me of not delivering, of bending under pressure or being unprincipled.”
Elsewhere, ex-community safety minister Ash Regan insisted she was in the SNP leadership contest to win it – despite being regarded as an outsider.
Ms Regan, who quit the Scottish government last year so she could vote against gender recognition reforms, accepted she was “probably the least well-known” of the candidates.
But she told the Sophy Ridge on Sunday programme on Sky News: “At the moment we understand that a large amount of the membership are still undecided, it is a very short contest.
“But I have had many people get in touch with me recently to say that they think I am the only hope for the SNP.”
Ms Regan said the country was at a crossroads but she would use any future Scottish or Westminster election as a means of establishing a majority for independence.
She added: “I believe I am the candidate setting out a credible, democratic means for Scotland to express its will at the ballot box and to give Scotland that choice over their own future.”
Among those who have confirmed their support for Mr Yousaf are the Scottish Constitution Secretary Angus Robertson and SNP Westminster deputy leader Mhairi Black.
Ms Forbes’ backers include veteran SNP MSPs Fergus Ewing, Annabelle Ewing and Christine Grahame as well as her campaign manager, Falkirk East MSP Michelle Thomson.
One of the party’s best known MPs, Joanna Cherry KC, has given her support to Ms Regan.
SNP members have been tasked with selecting a new leader – and thus a new first minister for the country at large.
And the three candidates to replace Nicola Sturgeon seem to have a rather different idea of who those party members actually are.
Humza Yousaf is betting that they are big fans of Ms Sturgeon and her legacy, and are chiefly interested in a continued focus on social justice issues.
Kate Forbes believes they are hungry for change from the current regime, are prepared to accept a more socially conservative leader and want more done for the economy.
And Ash Regan is basing her campaign on the thing that unites them all – independence. She is counting on their votes being guided by the impatience for action which was sometimes brought to bear on Nicola Sturgeon.
The fact the membership appears to have dropped from six figures to something closer to 78,000 – still a huge number amid Scotland’s population – underlines that nobody outside of SNP HQ is actually clear on what the core makeup of the party is any more.
Is the membership broadly young or old? Is it progressive or more traditional? Did hardcore independence supporters leave with Alex Salmond – or did others walk out amid the row over gender reform?
The outcome of the current contest may go some way towards answering those questions – but the three candidates seem to have drawn different conclusions already.
Source – BBC News