Jewish scholar David Daube offered the following possible background to the rending of the temple veil in light of Old Testament and Rabbinical traditions:
Mark tells us that, on Jesus's death, 'the veil of the temple was rent in twain from the top to the bottom'. Codex Bezae and the Itala are even more explicit: 'it was rent in two parts', not just 'in twain'.
Matthew and Luke both put the miracle together with others said to have occurred, the former with an earthquake and opening of graves, the latter with an eclipse of the sun. This, however, throws little light on the specific meaning of the event. As Luke pairs it off with the eclipse, the result is that, in his account, the rending of the veil precedes Jesus's death. But in looking for the original significance, we must start from Matthew and Mark, where it follows it. In modern literature, a good many interpretations are to be found, none of them satisfactory. The latest writer holds that the notice expresses an early theologoumenon of the Church, concerning the removal through Jesus's death of obstacles to God.
Most probably, we out to proceed from the actions of Elisha when Elijah ascended into heaven: 'And Elisha saw it and he cried, My father, my father, the chariot of Israel and the horseman thereof. And he took hold of his clothes and rent them in two pieces'. In Rabbinic times, there were prescribed occasions on which a man had to rend his garment. In this connection, the incident quoted acquired particularly importance. The Rabbis noted the emphatic 'he rent his clothes in two pieces' instead of a plain 'he rent his clothes'; and, in their usual manner, based on it the teaching that, in certain cases, the two parts into which you have rent your garment may never be sewn together again. The cases are the death of your father, your mother, your teacher of Torah, the Patriarch (Nasi) or the Father of the Court (Abh-beth-din), the receipt of terrible news, the utterance of a blasphemy, by someone in your presence, the burning of a Scroll of Law, and, finally, the destruction of Judaean cities, the temple of Jerusalem.
When we consider the stress laid in the New Testament on the complete splitting of the curtain into two--or, according to some readings, two parts--from top to bottom, it is safe to find here an allusion to the rite practised as a sign of deepest sorrow. We need not decide whether the death of Jesus is likened to that of a teacher of Torah or to the destruction of the temple. Either or both comparisons may play some part, as also the idea that those responsible for the crucifixion are the real blasphemers, and not Jesus at whose words the High Priest had rent his clothes. It may be noted that Luke, who places the rending of the veil before Jesus's death, thus completely obscuring its original import, omits this gesture by the High Priest. Presumably, he did not think his readers would understand the rite.
The question whether the miracle did in fact happen is not here relevant. We are concerned only with the manner of its representation, which connects it with a mourning rite--and, indeed, with the proto-type, in Rabbinic eyes of this rite, the action of Elisha on Elijah's ascension. It is difficult not to believe that this episode was in the mind of the author of the notice about the veil of the temple.
Support is furnished by the passages concerning the assumption of Jesus at the close of the gospels of Mark and Luke and at the beginning of Acts. True, the authors may no longer be conscious of a connection with the end of Elijah. But at some stage of the tradition such a connection no doubt existed. We need only compare the Lukan 'he was parted from them and carried up into heaven' with the description in the Old Testament, 'they parted them both asunder and Elijah went up into heaven'. The incident of the veil may be regarded as, in a way, adumbrating these references to the assumption.
Among the various explanations in early Christian literature, there is one--to be found in a work of Jewish-Christian provenance--which at least sees in the miracle of a sign of mourning, though not for Jesus's death but for the approaching end of the temple. Another point worth a mention is that the word pargdh, which in the Targum stands for the curtain separating the holy of holies from the outer chamber, may also denote a tunic. If the story originated in the Aramaic-speaking circles, the extension of the custom of rending one's garment to the veil of the temple--the tunic of the temple--must have been particularly easy.
So far we are on safe ground. May we go further? It is tempting to suggest that, in Matthew and Mark, the notice concerning the veil together with some verses, preceding and following its forms a much more closely knit pericope than has hitherto been realized. As Jesus cries out, 'Eli, Eli, lama sabachthani', some bystanders think he is summoning Elijah and mockingly remark, 'Let us see whether Elijah will come to save him,' After this, the rending in two of the veil of the temple, reminiscent as it is of what Elisha did when his master was translated, may well be intended as an answer to the mockery: here is Elijah himself, or one that is greater.
Even the centurion's confession may correspond to Elisha's cry, 'My father, my father, the chariot of Israel and the horseman thereof.' In the Targum, 'my father' is changed into 'my Rabbi', no doubt in deference to the view, recurring in Matthew, that, as a title, 'my father' is not ordinarily suitable for human beings. The rest is paraphrased by 'who was better for Israel by his prayer than chariots and horsemen'.
That the distinction was transferable to other prophets and teachers may be seen from the way king Joash addresses Elisha himself on his last sick bed, 'O my father, my father, the chariot of Israel and the horsemen thereof'; and, for Rabbinic times, from the Aramaic version of Chronicles, which speaks of 'Moses, the teacher of Israel, whose merit was better for them than horsemen and chariots', and from the story of the mast moments of Eliezer ben Hyrcanus (beginning of the 2nd cent. A.D.), on whose death his old antagonist Joshua ben Hananiah quoted the words of Elisha. The centurion's confession is rather different in substance, but its position at least may owe something to the old precedent. (David Daube, The New Testament and Rabbinic Judaism, 23-26)