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The Chinook crash killed all 29 people on board
The MPs have submitted two new reports by aviation experts to Defence Secretary George Robertson.
The five MPs, who include senior Labour backbencher Martin O'Neill, Tory defence spokesman Robert Key and Liberal Democrat defence spokesman Menzies Campbell, claim the evidence proves the two pilots should not have been blamed for the accident.
An official RAF Board of Inquiry found the 1994 crash - which claimed the lives of all 29 people on board, including 25 top Northern Ireland security experts - was caused by "gross negligence" by the pilots.
The finding has never been accepted by the families of the two men, Flt Lt Jonathan Tapper and Flt Lt Rick Cook.
The new evidence includes testimony provided by former RAF test pilot Sqn Ldr Robert Burke and Malcolm Perks, an expert in aviation computers.
Both have offered alternative scenarios, which they said provided a more likely explanation for the accident than pilot error.
They included a control "jam" caused by part of the flying controls becoming detached, and an engine "runaway up" due to a failure of the aircraft's computer software which could have caused the aircraft to enter low cloud over the island, becoming virtually uncontrollable.
Sqn Ldr Burke said that when he was in the RAF he had been ordered not to discuss the crash with anyone.
He said: "I have come to the conclusion that the verdict of `gross negligence' is totally unfair. It is unjust.
"If you blame the pilots, virtually everything else you can gloss over as a cause of the accident."
In his submission, Mr Perks described the Chinook's FADEC system as "high risk".
He also argued that the simulation used by the board of inquiry to recreate the accident had been "flawed".
Sara Cook, the widow of Flt Lt Cook, has described the verdict of the official inquiry as "scandalous."
She said: "There is now evidence the helicopter was unsafe to fly and that its appalling condition was the reason for the crash."
Pilot Jonathan Tapper's father, Michael Tapper, told BBC Radio 4's Today programme: "The reputation of any service officer is an important thing, particularly when it's a massive injustice like this.
"These two were first class pilots, some of the best in the world. To have this slur against their names is quite intolerable."
Mr Key said the new evidence covered mechanical and electronic matters, including the history of the aircraft in the weeks before the crash.
He said: "On the mechanical and electronic evidence there is doubt, and if there is doubt, these two dead pilots should not have been called grossly negligent.
"It's a question of miscarriage of justice. It's bad for morale if pilots think that, whatever they do, if they have a crash there is a chance they will be told they are grossly negligent."
Their presentation follows the decision of the Commons Defence Committee which found there was no evidence of "fundamental flaws" in the aircraft's design which caused the crash.