Formula One chiefs have asked for BAR-Honda to be disqualified from this year's championship at an appeal hearing in Paris on Wednesday.
BAR's season could rest on the hearing in Paris
Jenson Button's car was found to be five kilogrammes below the 600kg minimum weight at the San Marino GP.
"The FIA asks the court to exclude the BAR team from the world championship and to fine the team at least one million euros," a FIA statement read.
BAR say they are innocent and have asked the court to dismiss the appeal.
"At no time would I allow anybody in the team to do anything illegal, we have a common culture of integrity and fairness," BAR technical director Geoff Willis insisted.
A lesser penalty could see Button lose the six points he won in Imola.
FIA president Max Mosley said at the start of the season that any team found guilty of cheating would be thrown out of the championship.
"And it doesn't matter who it is, Ferrari or anybody in between, it has to be like that," he stated.
Officials from his organisation effectively accused BAR of cheating when claiming: "The team set out deliberately to gain an illegitimate and unfair advantage over other teams."
The FIA have disqualified a team in the past.
Tyrrell were banned from their last three races of the 1984 season and their results wiped out for the entire season because they were adding lead shot to the car as ballast during races.
Toyota were also axed from the World Rally Championship in 1995 for using an illegal turbo-charger.
Team principal Nick Fry hopes BAR will not suffer the same fate, saying: "We are hanging on the basic belief that right will prevail at the end.
"At no time was the car light and I don't think that we've done anything wrong."
The FIA believes BAR were using two hidden fuel tanks within the main tank to hide fuel that was used as ballast during the race.
That would allow the car to run lighter than its rivals - and dip below the minimum weight limit in the laps immediately preceding its fuel stop.
It could also be used to allow the team to do more laps before a stop, giving them a strategic advantage in the race.
But the team says the extra tanks are used to pressurise fuel before it is injected into the engine
The lawyer representing BAR at the hearing, David Pannick said: "There was no secret chamber in this engine. At worst, there was a minor misunderstanding. A modest fine would suffice."
But the general secretary of the FIA, Pierre de Coninck, who was presiding over the hearing, said: "A flexible fuel compartment allows a car to stay out for two or three laps when a legitimate car would have to pit.
"This enables cars to complete more laps than a genuine 600kg car."
Kris De Groot, a member of the Formula One technical team, told the hearing he asked BAR's chief mechanic Alistair Gibson for a "full draining" of the car.
He said he then found more fuel, as well as a plastic tube, the function of which was not clear.
"Most teams understand the term 'full drain'," De Groot said. "I asked Gibson what the tube was for and I was given no definitive answer."
The verdict will be announced on Thursday.