The Serious Fraud Office (SFO) case centres on alleged undisclosed payments to Qatar in return for cash that helped the bank during the financial crisis.
Roger Jenkins, Tom Kalaris, and Richard Boath all deny wrongdoing.
Former Barclays chief executive John Varley, their co-defendant in a previous trial, was acquitted in June.
The SFO’s criminal proceedings against the bank itself were also dismissed by a court last year. Mr Varley and Barclays had each denied wrongdoing.
Mr Jenkins, 64, was the chairman of investment banking in the Middle East, while Mr Kalaris, 63, headed the wealth division and Mr Boath, 60, led the European corporate finance arm.
The trio is each charged with conspiracy to commit fraud by false representation and fraud by false representation.
The case centres on claims of secret payments to Qatar as part of a deal to raise more than £11bn ($13.6bn) from investors in two tranches in June and October 2008.
It is claimed that these multi-million pound payments to investors, including to the then prime minister of the Gulf state, Sheikh Hamad bin Jassim bin Jabr al-Thani, were not property disclosed to the markets.
The cash injection from Qatar helped Barclays avoid the government bailout fate of High Street rivals, including Royal Bank of Scotland.
The defendants were charged in 2017 after the SFO spent years investigating the allegations. The trial is regarded as a high stakes case for the SFO, which has been accused of failing to pursue companies and individuals over their part in the financial crisis.
The charges against Mr Jenkins relate to his involvement in the June and October Qatar fundraisings. The cases of the two other men relate to the June fundraising only.
Monday’s Old Bailey trial will start with jury selection, and the case is expected to last several months.