The doctrine of "annihilation" is the idea that eventually, after a sufficient period of punishment, the souls of the wicked will go out of existence. This dogma is without biblical support.
The punishment of those who die estranged from God is described as: "fire unquenchable" (Mt. 3:12). Final punishment is a state where "their worm dies not," and the "fire is not quenched" (Mk. 9:48). The wrath of God "abides" (present tense -- keeps on abiding) of the lost person (Jn. 3:36).
Various figures are employed in connection with the words "forever" or "everlasting" (e.g., chains, contempt, destruction, torment; see Dan. 12:2; Mt. 18:8; 25:41, 46; 2 Thes. 1:9; Jude 6-7; Rev. 14:11; 19:3; 20:10). It is not the mere effect of punishment that is eternal, but the actual punishment itself (Mt. 25:46).