The official cause for the accident as reported by the governments of France and the USSR
claimed pilot error. However, the possibility that is considered to be the strongest is that a Mirage fighter jet was escorting the plane and the pilot put the plane on a risky manoeuvre, the wings overstressed and snapped. Another more recent hypothesis is that the pilot of the Tupolev was not warned about the presence of the Mirage and panicled when he noticed it coming closer.
It is also speculated that Tupolev engineers tweaked the plane before the show in order to outperform Concorde but the crew didn't know of such changes.
[Edited 2005-04-25 10:35:17]