Pope Benedict XVI stepped down last month after nearly eight years in office, becoming the first pontiff to resign in 600 years.
The 85-year-old blamed his failing health for his inability to carry on.
Under the rules of the secret ballot, or conclave, cardinals will vote until one achieves a two-thirds majority.
Correspondents say no one candidate stands out as Benedict XVI’s likely successor.
Stoves going in
The vote will be preceded by Mass on Tuesday morning, with the first ballot due in the afternoon, the Vatican press office said.
Vatican staff have been preparing the Sistine Chapel, where the conclave will take place, installing the two stoves that will produce white smoke from burnt ballot papers when a new pope is elected.
The last election in 2005 took three days, and correspondents say the number of meetings this time is being seen as a reflection of the many challenges facing the Church.
Despite the vows of secrecy, Italian newspapers have been publishing what they say are leaked details of debate among cardinals on problems faced by the Church.
Reform of the Vatican’s bureaucracy – known as the Curia – and the Vatican bank have both been on the agenda, the reports say.
Last year, European regulators said the bank was not doing enough to combat money laundering, while intrigue in the Vatican was revealed by documents leaked by Pope Benedict’s butler.
US Cardinal Timothy Dolan wrote on a blog that most of the discussions covered preaching and teaching the Catholic faith, tending to Catholic schools and hospitals, protecting families and the unborn, and supporting and recruiting priests.
“Those are the ‘big issues’,” he wrote.
“You may find that hard to believe, since the ‘word on the street’ is that all we talk about is corruption in the Vatican, sexual abuse, money. Do these topics come up? Yes! Do they dominate? No!”
During Benedict’s reign the Catholic Church was wracked by a worldwide scandal over the sexual abuse of children by priests.
There are also tensions between traditionalists and reformers over issues including priestly celibacy, gay rights and the role of women.