If a simple majority votes in favour, as is expected, Ms Rousseff will be automatically suspended from office.
Ms Rousseff made a last-ditch appeal to the Supreme Court to stop proceedings, but the move was rejected.
The president is accused of illegally manipulating finances to hide a growing public deficit ahead of her re-election in 2014, which she denies.
The debate has been running for hours. Sixty-eight senators originally registered to speak and two more added their names to the list during the proceedings, bringing the total to 70.
By 21:15 local time (00:15 GMT), 30 senators had spoken. Of those, 24 spoke in favour of an impeachment trial and six against.
Senator Fatima Bezerra from Ms Rousseff's Workers's Party said she would "vote against this farce".
"Those who back this coup d'etat won't ever be forgiven," she warned.
The other senators to back Ms Rousseff were Jorge Viana and Angela Portela, also of the Workers' Party.
But there were also three senators from other parties who opposed the impeachment.
They were Temario Mota of the Democratic Workers' Party, Randolfe Rodrigues of REDE and Roberto Requiao of the PMDB.
Senator Viana called the impeachment proceedings "institutional anarchy" while Senator Mota said that "this impeachment was born of revenge, hatred and revenge".
Among those who backed the impeachment trial was Aecio Neves, who lost to Ms Rousseff in the 2014 presidential election.
Earlier, former football player Romario, who is now a senator for the Brazilian Socialist Party, also referred to Brazil's economic problems, calling it "a very serious crisis".
Senator Romario speaks during the session debating the voting for the impeachment of President Dilma Rousseff in Brasilia, Brazil, Brazil, May 11, 2016
Football star-turned-senator Romario said he would vote in favour of the impeachment trial
Senator Jose Agripino Maia accused the governing Workers' Party of "getting too accustomed to spending" beyond its means.
One of the most passionate speakers in favour of the impeachment trial was Magno Malta of the Party of the Republic.
He compared the government of Ms Rousseff to "gangrene" which needed to be removed to make Brazil healthy again.
But the atmosphere in the upper house is a far cry from the packed lower house session on 17 April.
The session in the Senate has been a lot calmer than that in the lower house on 17 April
Many seats are empty and senators can be heard chatting amongst themselves while the speeches are going on.
Mr Calheiros called the senators to order and told them to "pay attention and put their phones away".
A critical moment: Analysis by Wyre Davies, BBC Brazil correspondent
Brazilian President Dilma Rousseff (centre) has vowed to fight to the end
What has been a long, damaging and divisive political process is at a critical moment as the 81 members of the Brazilian Senate prepare to vote on whether or not to subject Dilma Rousseff to a full impeachment trial.
The beleaguered president denies the charges against her - that she illegally concealed the scale of the budget deficit. Brazil's first female leader says that what is really happening, first in the lower house of Congress and now in the Senate, is a judicial coup by her political opponents to remove her from office.
Whatever the real reasons for impeachment, there is no doubt that Ms Rousseff's leftist Workers' Party is deeply unpopular, with Brazil in the middle of an economic crisis and her government embroiled in a huge corruption scandal.
In a recent interview with the BBC, Ms Rousseff appeared to acknowledge that she would be suspended pending an impeachment trial but she said would fight to clear her name and fully intended to resume the final two years of her presidency.
If the vote goes against her, Ms Rousseff will be replaced by Vice-President Michel Temer while the impeachment trial lasts.
She says Mr Temer is a traitor who is taking part in a political coup against her democratically elected government.
Her chief of staff, Jaques Wagner, said Ms Rousseff was "outraged by the injustice committed against her, but standing firm awaiting the Senators' decision.
Ms Rousseff and her chief of staff, Jaques Wagner, could be seen looking out from a window in the presidential palace
She has promised to fight to the end.
"I will not resign. That never crossed my mind," she said during a speech at a women's rights conference in the capital Brasilia on Tuesday.