Answer
The Bible does not tell us precisely what our bodies will be like, although it does tell us our bodies will be the same bodies. Our bodies will be "resurrected" or "raised," not "replaced." The fullest mention we have of the nature of our new bodies is in 1 Corinthians 15. The best example we have as to what our new bodies will look like, however, is Jesus. Jesus was the firstfruits of the resurrection (1 Cor. 15:20,23), meaning that his resurrection is the first of many who will be resurrected like him (the resurrection of believers). Jesus' resurrected body had unusual properties (suddenly appearing in a locked room, Luke 24:36), but it still was a human body (arms, legs, etc.) which could eat (Luke 24:41-43) and be touched (Luke 24:39; John 21:13). He was also clearly identifiable (John 21:7; Luke 24:36-37) -- the reason he was not recognized on the road to Emmaus was that the eye's of the other men were blinded to his identity, not that Jesus' body was not recognizable (Luke 24:16).
Without going into too much detail, I would add that the biblical picture of man is as a body-soul being. That is, our bodies are intrinsic parts of our beings. The implication of this is that we would not be ourselves if we did not have the same bodies (however perfected) in heaven. There must be as much continuity between the bodies we have now and the bodies we have in the future as there is between the souls we have now and the souls we will have in the future. This is why our salvation is not considered complete until we have fully participated in the resurrection (Rom. 8:23-25).
Answer by Ra McLaughlin
Ra McLaughlin is Vice President of Finance and Administration at Third Millennium Ministries.