There is much support for an eternal or everlasting hell. This belief has been taught by many churches for centuries and a superficial reading of the Bible could lead to this conclusion.
And these shall go away into everlasting punishment: but the righteous into life eternal. Matthew 25:46
The sinners in Zion are afraid; fearfulness hath surprised the hypocrites. Who among us shall dwell with the devouring fire? who among us shall dwell with everlasting burnings? Isaiah 33:14
There are 48 references in the KJV to "eternal" (which includes "eternity") most of them refer to good things, especially "life" ie "eternal life" or "life eternal" or eternal power, glory, salvation, inheritance etc.. A few refer to hell, such as Mark 3:29, "eternal damnation" and Jude 7, "eternal fire".
There are 54 references to "hell". Only Mark 9 leads one to the conclusion that it may be eternal, because the fire "is not quenched":
And if thy hand offend thee, cut it off: it is better for thee to enter into life maimed, than having two hands to go into hell, into the fire that never shall be quenched: Where their worm dieth not, and the fire is not quenched. And if thy foot offend thee, cut it off: it is better for thee to enter halt into life, than having two feet to be cast into hell, into the fire that never shall be quenched: Where their worm dieth not, and the fire is not quenched. And if thine eye offend thee, pluck it out: it is better for thee to enter into the kingdom of God with one eye, than having two eyes to be cast into hell fire: Where their worm dieth not, and the fire is not quenched. Mark 9:43-48
Matthew lends further credence:
Wherefore if thy hand or thy foot offend thee, cut them off, and cast them from thee: it is better for thee to enter into life halt or maimed, rather than having two hands or two feet to be cast into everlasting fire. Matthew 18:8
Then shall he say also unto them on the left hand, Depart from me, ye cursed, into everlasting fire, prepared for the devil and his angels: Matthew 25:41
And these shall go away into everlasting punishment: but the righteous into life eternal. Matthew 25:46
Who shall be punished with everlasting destruction from the presence of the Lord, and from the glory of his power; 2 Thessalonians 1:9
This false theory first assumes the incorrect belief that the fire is literal (see "The Lake of Fire"). It is spiritual NOT physical.
Secondly, it assumes a physically impossible belief that wicked, physical bodies are immortal, being able to withstand physical flames for ever. But immortality is not given to sinners, without glorification and salvation. It is only given to the pure and saved.
Jude calls the fire of Sodom and Gomorrha "eternal", but we know those fires are NOT burning now.
Even as Sodom and Gomorrha, and the cities about them in like manner, giving themselves over to fornication, and going after strange flesh, are set forth for an example, suffering the vengeance of eternal fire. Jude 7
The solution to this apparent discrepancy is by correctly understanding the Hebrew and Greek words translated "eternal" or "everlasting" in the King James English translation. Young, in his Literal translation, translates these words as "age"
See "The End of "Eternity" and "ages" explained and unmasked in "Aions or Eons".
Now we can conclude that Hell is NOT eternal.