In the first century Judaisms, there seems to have been a widespread belief that a soul exists eternally before being placed in a mortal body. After death, the righteous are given new bodies and the wicked are condemned to suffering. In Matthew 16:14 it seems that the popular view of the afterlife might also have included reincarnation into new, mortal bodies--for great prophets at least.

Yeshua hinted at a similar idea when he said that John the Baptist was Elijah, but he probably didn't mean it literally. John had come in the office and power of Elijah, but he wasn't Elijah himself. Yeshua never validated either belief (per-incarnation and re-incarnation) in his teachings.