The teaching of the Bible and the early church relative to cremation is a bit vague. Ultimately, burial customs reflected the worship of God in the context of cultural norms.
Does the Bible talk about cremation?
It is true that the Jewish custom was burial—specifically, to bury the body in a cave until insects and the elements had stripped the flesh, then to bury the bones in a more permanent location. Cremation is not mentioned in the Bible, although immolation was sometimes the penalty for law-breakers (Genesis 38:24; Leviticus 20:14; 21:9; Numbers 16:35; Joshua 7:15-25). The only biblical instance of dead bodies being burned is in 1 Samuel 31:11-13. The bodies of Saul and his sons were burned out of respect (the Philistines had mutilated the bodies). The bones were then buried in honor. To be refused burial, in particular to have one's body eaten by wild animals, was a great dishonor (1 Kings 13:22; Jeremiah 16:6).
Burial is exemplified, but not demanded, in the Old Testament, and cremation is not expressly forbidden in Scripture. Instead, it is the Talmud—an extra-scriptural commentary—that prohibits cremation as the mutilation of a corpse.
The early church rejected cremation, mirroring their rejection of pagan philosophy. A popular false doctrine of the day was Gnosticism, which taught that the physical was evil and the spiritual was good. This belief made cremation desirable, since it completely destroyed the physical body and freed the spirit from its earthly bond. The early church rejected Gnosticism and its view of the body. The Scriptures teach that God made the body and it was good (Genesis 1:31). In addition, the Bible speaks of the body as the home of the Holy Spirit (Romans 8:9) and promises the resurrection of the body (1 Corinthians 15:51-52). The early Christians honored the bodies of the dead, showing them respect as "jars of clay" (2 Corinthians 4:7). This doesn't mean they believed the physical body must remain intact for resurrection to occur; just that cremation was a metaphorical rejection of God's blessing on the physical part of us.
Some modern views reflect similar thinking. Many religious people still favor "Christian burial" over cremation. In Judaism, cremation is more abhorrent than ever, as it is reminiscent of how bodies were disposed of in the Holocaust. Among the general populace, however, cremation has grown in popularity in recent years. Factors such as expense and land usage favor cremation.
The early church saw burial as an expression of faith in Jesus' redemption of the physical body. However, burial is not scripturally mandated. First Corinthians 15:35-55 explains that our physical body is a mere seed, and God will raise for us an imperishable, glorious, spiritual body. As long as the intent is glorifying to God, it doesn't matter if a body is buried or cremated.
Death - What does the Bible say about it?
What happens after death?
Is there really an afterlife?
Is the human soul mortal or immortal?
Christian Eschatology - What is it?
Truth about Humanity