The pair are accused of falsifying the paperwork at the height of the Swedish company's financial difficulties at the start of the decade.
A third person – who has not been named in the Swedish media – is accused of assisting them by issuing false invoices adding up to a total of 30 million kronor ($3.55m).
According to court documents, the charges relate to the firm's business in Ukraine and the paperwork in question was signed just before former CEO Jan Åke Jonsson resigned.
Both Jonsson and Saab's former head lawyer Kristina Geers have admitted signing the papers but denied knowledge of the Ukranian firm implicated in the case.
All three suspects deny all the charges against them.
Saab's former head lawyer Kristina Geers. Photo: Björn Larsson Rosvall/TT
Saab filed for bankruptcy at the end of 2011, after teetering on the edge of collapse for nearly two years.
Chief prosecutor Olof Sahlgren told the court in Vänersborg on Wednesday that the alleged crimes took place in March 2011, when Saab was briefly owned by the Dutch company Spyker Cars.
It was eventually bought by National Electric Vehicle Sweden (Nevs), a Chinese-owned company after hundreds of staff lost their jobs.
The car maker, which is based in west Sweden, has struggled to resolve serious financial difficulties by attracting new investors since the takeover.
In October 2014 it announced it had axed 155 workers, close to a third of its workforce.
Since 2000, Saab automobile has had no connection with the defence and aeronautics firm with the same name. It only produces one model today, the electric 9-3 Aero Sedan, mainly targeting the Chinese market.
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