It is allowed only in some circumstances, for practical reasons (e.g. infectious diseases, local civil regulations, lack of space - not an American problem this one! - or other very special and rare occasions)but ONLY IF it is clear and certain that there was no intention of denying the resurrection of the body.
Of course God can resurrect the bodies of those died millennia ago and now turned into ash, but since the very beginning the Church prohibited cremation to fight the pagan notion of death and to instill faith in resurrection.
It's permitted (but somewhat frowned upon) unless it's done to deny the dogma of the resurrection of the body.
My father was cremated, because it's much cheaper and he didn't want much money spent on his funeral.
Out of curiosity, when is cremation allowed in the Catholic Church?In addition to the reasons already given, cremation is allowed when the body is sent to another state for burial. For example, after my brother's funeral in New York, my sister-in-law had his body cremated, and the "cremains" (that's what the funeral director called them!) were sent to New Hampshire for internment in the family plot.
2301 Autopsies can be morally permitted for legal inquests or scientific research. The free gift of organs after death is legitimate and can be meritorious.
The Church permits cremation, provided that it does not demonstrate a denial of faith in the resurrection of the body.93
93 Cf. CIC, can. 1176 § 3.
TITLE III: CHURCH FUNERALS
Can. 1176 ß1 Christ's faithful who have died are to be given a Church funeral according to the norms of law.
ß2 Church funerals are to be celebrated according to the norms of the liturgical books. In these funeral rites the Church prays for the spiritual support of the dead, it honors their bodies, and at the same time it brings to the living the comfort of hope.
ß3 The Church earnestly recommends that the pious custom of burial be retained; but it does not forbid cremation, unless this is chosen for reasons which are contrary to Christian teaching.