In early times, Romans cremated their dead as a rejection of an afterlife, a direct contradiction to the Christian hope of resurrection. For this reason, cremation was associated with pagans and Christians forbade it in favor of traditional burial. For nearly two thousand years, cremation was not permitted by the Catholic Church.
Early Christians believed what we profess today. We are an incarnational people who believe creation is holy because, "The Word became flesh and made His dwelling among us" (John 1:14). God is not somewhere "up there" but within. As God is in us, we "a temple of the Holy Spirit: (1 Corinthians 6:19) and the body are to be treated with respet both in life and after death.
The Church approved cremation during the Vatican II reforms of the funeral and burial rite. The Congregation for the Doctrine of Faith issued a statement of clarity and further directives.
"Cremation does not affect the soul, nor does it prevent God from raising up the deceased body to new life."
When a Catholic is cremated, his/her ashes must be kept intact, not scattered on land or sea. The ashes must be separated but placed within a proper vessel and be interred in a sacred burial plot, columbarium, or mausoleum.
To read the original Vatican Documents on Cremation, go to: https://www.vatican.va/roman_curia/congregations/cfaith/documents/rc_con_cfaith_d