Objection 1. It would seem that the bodies of the damned will be corruptible. For everything composed of contraries must necessarily be corruptible. Now the bodies of the damned will be composed of the contraries whereof they are composed even now, else they would not be the same, neither specifically nor, in consequence, numerically. Therefore they will be corruptible.
Objection 2. Further, if the bodies of the damned will not be corruptible, this will be due either to nature, or to grace, or to glory. But it will not be by nature, since they will be of the same nature as now; nor will it be by grace or glory, since they will lack these things altogether. Therefore they will be corruptible.
Objection 3. Further, it would seem inconsistent to withdraw the greatest of punishments from those who are in the highest degree of unhappiness. Now death is the greatest of punishments, as the Philosopher declares (Ethic. iii, 6). Therefore death should not be withdrawn from the damned, since they are in the highest degree of unhappiness. Therefore their bodies will be corruptible.
On the contrary, It is written (Apocalypse 9:6): "In those days men shall seek death, and shall not find it, and they shall desire to die, and death shall fly from them."
Further, the damned will be punished with an everlasting punishment both in soul and body (Matthew 25:46): "These shall go into everlasting punishment." But this would not be possible if their bodies were corruptible. Therefore their bodies will be incorruptible.
I answer that, Since in every movement there must needs be a principle of movement, movement or change may be withdrawn from a movable in two ways: first through absence of a principle of movement, secondly through an obstacle to the principle of movement. Now corruption is a kind of change: and consequently a body which is corruptible on account of the nature of its principles may be rendered incorruptible in two ways. First by the total removal of the principle which leads to corruption, and in this way the bodies of the damned will be incorruptible. For since the heaven is the first principle of alteration in virtue of its local movement, and all other secondary agents act in virtue thereof and as though moved thereby, it follows that at the cessation of the heavenly movement there is no longer any agent that can change the body by altering it from its natural property. Wherefore after the resurrection, and the cessation of the heavenly movement, there will be no quality capable of altering the human body from its natural quality. Now corruption, like generation, is the term of alteration. Hence the bodies of the damned will be incorruptible, and this will serve the purpose of Divine justice, since living for ever they will be punished for ever. This is in keeping with the demands of Divine justice, as we shall state further on (3), even as now the corruptibility of bodies serves the purpose of Divine providence, by which through the corruption of one thing another is generated.
Secondly, this happens through the principle of corruption being hindered, and in this way the body of Adam was incorruptible, because the conflicting qualities that exist in man's body were withheld by the grace of innocence from conducing to the body's dissolution: and much more will they be withheld in the glorified bodies, which will be wholly subject to the spirit. Thus after the general resurrection the two aforesaid modes of incorruptibility will be united together in the bodies of the blessed.
Reply to Objection 1. The contraries of which bodies are composed are conducive to corruption as secondary principles. For the first active principle thereof is the heavenly movement: wherefore given the movement of the heaven, it is necessary for a body composed of contraries to be corrupted unless some more powerful cause prevent it: whereas if the heavenly movement be withdrawn, the contraries of which a body is composed do not suffice to cause corruption, even in accordance with nature, as explained above. But the philosophers were ignorant of a cessation in the heavenly movement; and consequently they held that a body composed of contraries is without fail corrupted in accordance with nature.
Reply to Objection 2. This incorruptibility will result from nature, not as though there were some principle of incorruption in the bodies of the damned, but on account of the cessation of the active principle of corruption, as shown above.
Reply to Objection 3. Although death is simply the greatest of punishments, yet nothing prevents death conducing, in a certain respect, to a cessation of punishments; and consequently the removal of death may contribute to the increase of punishment. For as the Philosopher says (Ethic. ix, 9), "Life is pleasant to all, for all desire to be... But we must not apply this to a wicked or corrupt life, nor one passed in sorrow." Accordingly just as life is simply pleasant, but not the life that is passed in sorrows, so too death, which is the privation of life, is painful simply, and the greatest of punishments, inasmuch as it deprives one of the primary good, namely being, with which other things are withdrawn. But in so far as it deprives one of a wicked life, and of such as is passed in sorrow, it is a remedy for pains, since it puts an end to them. and consequently the withdrawal of death leads to the increase of punishments by making them everlasting. If however we say that death is penal by reason of the bodily pain which the dying feel, without doubt the damned will continue to feel a far greater pain: wherefore they are said to be in "everlasting death," according to the Psalm (48:15): "Death shall feed upon them."
Source: Summa Theologica (New Advent)