The answer to this question is very simple, but it does have some intricacies to be aware of. Our own Parish has installed a Columbarium and due to the popularity is planning to expand it in the near future.
From: Catholic Answers
Early Christians opposed cremation because pagans often cremated their dead as a sign of disdain for the Christian’s belief in the physical resurrection of the body. To protect belief in this doctrine of faith, the Church forbade cremation. That prohibition was lifted in 1963.
The Church still recommends that the faithful be buried, but Catholics may be cremated so long as cremation does not demonstrate a denial of belief in the resurrection of the body (CCC 2301).
Karl Keating
The following is Excerpted from United States Catholic Catechism for Adults
CHRISTIAN DEATH
We do not like to think about death. There is much in our culture that distracts us from reflection about our final destiny. We are encouraged to think only about the present moment and to fulfill today’s needs. But the Christian embraces the total reality of life and God’s call to the fullness of life after death. Thus, for example, Christians assist those whose earthly journey is coming to an end. “The dying should be given attention and care to help them live their last moments in dignity and peace. They will be helped by the prayer of their relatives, who must see to it that the sick receive at the proper time the sacraments that prepare them to meet the living God” (CCC, no. 2299).
Not only do we care for the dying to help them pass their final moments in dignity and peace, but we also maintain reverence for their bodies once they are deceased. “The bodies of the dead must be treated with respect and charity, in faith and in the hope of the Resurrection. The burial of the dead is a corporal work of mercy [cf. Tb 1:16-18]; it honors the children of God, who are temples of the Holy Spirit” (CCC, no. 2300). The rituals accompanying respect for the dead include the funeral vigil (wake), the funeral itself, and the burial of the body or the cremated remains of the deceased at the cemetery. Participation in these rites enables friends and others to demonstrate reverence for the deceased, to pray together for the eternal repose of the deceased, and to give the family of the deceased prayerful support.
For further research please follow these links:
USCCB
Bereavement And Funerals
Cremation And The Order Of Christian Funerals
Reflections On The Body, Cremation, And Catholic Funeral Rites
Also: Cremation Resource