What is the shelf life of unopened Hunt's tomato paste?

It is reasonable to expect 3 or 4 years from canning, even though the "best if used by" date is usually only 2 year from canning.

However commercially canned foods have been opened more than 50 years after canning are usually still perfectly safe to eat, but color and flavor usually have changed some. Commercial canning is one of the safest ways to preserve foods for long term storage.