The Catholic Church no longer forbids cremation, and it has been gaining in popularity. See this article.

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...The new (1983) stipulates, "The Church earnestly recommends that the pious custom of burying the dead be observed; it does not, however, forbid cremation unless it has been chosen for reasons which are contrary to Christian teaching" (No. 1176, 3). Therefore, a person may choose to be cremated if he has the right intention. However, the cremated remains must be treated with respect and should be interred in a grave or columbarium.

A pastoral problem occurs concerning the funeral Mass itself. The cremated remains can not be present during the vigil or wake service, or during the Mass, since the regular liturgical prayers and actions are designed to honor the body. The body best reminds us of that person who entered a new life at baptism, becoming a "Temple of the Lord," and has now gone, we hope and pray, to the fulfillment of that life and eternal rest. On the other hand, ashes remind us of the corruptibility of the deceased.

As a priest, I believe that the entire Catholic funeral liturgy—the vigil service, the Mass of Christian Burial and the Final Committal and Burial—offers to us a great reminder of our faith and aids in our healing. The death of someone we love is always hard to face; however, there is something good and comforting when we gather as a faith community in the presence of our Lord and the body of the deceased, and offer that loved one back to God. Unfortunately, on more than one occasion I have dealt with families who have had the deceased loved one cremated, and later regretted the action, even feeling great guilt. I always recommend for people who want to be cremated or want to have their deceased loved one cremated that they do so after the funeral Mass and then inter the remains properly.
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