While the Bible never addresses reincarnation specifically, it is clear that the biblical model of life, death, and afterlife is incompatible with any form of reincarnation as posited in religions such as Hinduism, Buddhism, and certain New Age or Neo-Pagan belief systems. In Hebrews 9:27–28, we are told that “just as it is appointed for man to die once, and after that comes judgment, so Christ, having been offered once to bear the sins of many, will appear a second time, not to deal with sin but to save those who are eagerly waiting for him.” This passage alone appears to eliminate the possibility of reincarnation.
Along the same lines, in Luke 23:43 Jesus tells the thief on the cross that he will be with Christ in paradise that very day, which assumes that the man will not be reincarnated back into earthly life. Similarly, passages such as James 4:14, which discuss the temporal nature of human life are inconsistent with a reincarnationist idea of living earthly lives over and over for centuries, millennia, or all eternity. On top of all this, if human souls were reincarnated over and over, then how could some people in the Bible see the spirits of long dead people, like Moses being seen by the apostles in Matthew 17:3 during the transfiguration of Christ?
But what are we to do with those who claim they have memories of their past lives? The first and perhaps most important question we should ask is whether or not these “memories” are genuine. Human memory is notoriously unreliable (just ask any lawyer or detective), and people frequently misremember things, believing they remember things that never actually happened or not remembering things that did happen. In the case of those claiming to remember their past lives, one can easily imagine them misremembering images from TV shows or movies, mental fantasies from books they read years earlier, or mistaking dreams for genuine memories. How can we know with any certainty that their past-life memories are not one of these things? Is it really more logical to assume that their memories are genuinely from past lives rather than one of these other things? While some modern “past-life experts” claim to find evidence for reincarnation by connecting things like phobias and physical ailments in currently living people with traumatic events in past lives, the past-life “experts” are assuming the existence of a past-life (or past-lives) in explaining current health problems, not showing that those past lives actually happened.
The fact of the matter is that there is simply no solid, scientifically acceptable evidence that the memories of past lives claimed by some people are genuine, rather than misremembered events or simply make-believe. Ultimately, the question comes down to whether we will find Truth in the unreliable minds and memories of fallen and fallible human beings or from the timeless, holy Word of God. Christians can confidently assert that reincarnation is not a possibility for the human soul; when this life ends, our eternity in the afterlife begins.
 Got Questions Ministries. (2010). Got Questions? Bible Questions Answered. Bellingham, WA: Logos Bible Software.