I have not done a detailed study of this issue but here are some thoughts. While there is no New Testament passage that actually forbids cremation, it seems clear that neither the Old Testament Jews nor the New Testament Christians cremated their dead. Rather, they washed the body, wrapped it in clean cloths with spices, and placed it in the ground or in a tomb.
While there may be some situations when cremation is the better way to dispose of the body, for the most part, Christians have typically preferred burial. This is the way our Lord’s body was handled after His death (Matt. 27:57–61), and Paul seems to teach burial in 1 Corinthians 15:35–46.
In Old Testament times, burning the body was a punishment fit for a criminal (Lev 20:14; 21:9; Josh 7:25). To show the attitude of Jews toward cremation, the Mishna forbade cremation as idolatry (‘Abodah Zarah I.3).