What of Matthew's account of the guards? He records that the tomb was guarded (Mt 17:62-6), that the guards fled when the angel appeared (Mt 28:4) and that they were subsequently bribed to say that the disciples had stolen the body while they were asleep. He also comments that this allegation was still current amongst the Jews at the time of writing (Mt 28:11-5).
Some say that Matthew added this in order to bolster the resurrection story against the allegation of body-snatching. But that is hardly likely to have been the case, since Matthew records that the guard was not set until the day after the crucifixion: if he had been making the story up it would have been much more convincing if the tomb had been sealed and guarded from day one.
Also, if he were trying to bolster his story, why would he deliberately introduce the suggestion that the body had been stolen by the disciples?
One thing may be said with reasonable certainty however: Matthew's account is strong testimony that the body really had disappeared and that such reports must have been in circulation.
Is there any independent corroboration of the missing corpse or the guard's story? From Jewish sources, no; many ancient Jewish references to Jesus are known to have been expurged from Jewish writings on account of Christian persecutions in later centuries. But we do have one very interesting piece of evidence.
In 1878 an inscribed marble slab was found, dated by experts to the reign of Claudius Caesar, sometime between AD 44 and AD 54:
'Ordinance of Caesar. It is my pleasure that graves and tombs remain perpetually undisturbed for those who have made them for the cult of their ancestors or children or members of their house. If, however, anyone charges that another has either demolished them, or has in any other way extracted the buried, or has maliciously transferred them to other places in order to wrong them, or has displaced the sealing on other stones, against such a one I order that a trial be instituted, as in respect of the gods, so in regard to the cult of mortals. For it shall be much more obligatory to honour the buried. Let it be absolutely forbidden for anyone to disturb them. In case of violation I desire that the offender be sentenced to capital punishment on charge of violation of sepulchre.'
The slab was not found at a major Roman site, but a small Jewish village: one so obscure it's not mentioned in Josephus' lists of Israel's towns and villages, nor in the Talmud. (Some modern scholars even claimed no place of this name existed in New Testament times; until 1962, that is, when its name was found in an inscription of the period from Caesarea.)
Why should Claudius have posted such a notice in such an obscure place? Could it be something to do with its name...