We are told in the parable of the sheep and goats (Matt. 25:31-46) that those whom the judge rejects go away into Kolasis (punishment) aionios (a final state). The phrase is balanced by the reference to zoe aionios (eternal life) which is also a fixed and final state. Even if this word aionios is believed to mean only "belonging to the coming aion", and not to imply endlessness in the sense of perpetual continuity, the thought of endlessness is certainly bound up in the phrase "eternal life," and can hardly therefore be excluded from the corresponding and balancing phrase "eternal punishment." The idea that in this text aionios as applied to kolasis must imply everlastingness seems to be unbreakable.
The New testament always conceives of this eternal punishment as consisting of an agonizing knowledge of one's own ill desert, of God's displeasure, of the good that one has lost, and of the irrevocable fixed state in which one now finds oneself. The doctrine of eternal punishment was taught in the synagogue even before our Lord took it up and enforced it in the Gospels. All the language that strikes terror into our hearts weeping and gnashing of teeth, outer darkness, the worm, the fire, gehenna, the great gulf fixed is all directly taken from our Lord's teaching. It is from Jesus Christ that we learn the doctrine of eternal punishment.
Study the following Bible passages and any other relevant ones on this topic, and reach your own conclusions, prayerfully: Luke 16:26; John 3:18-19, 36; 5:29; 12:32; Acts 3:21,23; Rom. 1:16, 5:18-21; 1 Cor. 15:25-28; 2 Cor. 5:10, 19; 6:2; Gal. 1:4; Eph. 5:25; Phil. 2:9-11; 1 Tim. 2:4; Titus 2:11; Heb. 2:9; 9:27; 1 Pet. 3:19; 2 Pet 3:9; 1 John 1:5; 2:2; 4:8.