Romans 6:23 For the wages of sin is death, but the free gift of God is eternal life in Christ Jesus our Lord.
I believe eternal punishment for the non-believer means eternal death. Their death is forever and ever, as opposed to those in Christ having life forever and ever.
In the passage above, it is death that is contrasted with life.
A man named William Fudge has written a couple of really good, thorough books on this subject, The Fire that Consumes, and Hell, A Final Word.