Pauly Shore was considered for the role of Link before the producers met Brendan Fraser and decided that he was better suited for the part. However, they liked Shore so much that they created the role of Stoney just for him. Most of Stoney's lines were ad-libbed by Shore because they were never in the original script.
At 6'3", Brendan Fraser was actually too big for the clothing that costume designer Marie France had originally purchased for him. Since Fraser's outfits were supposed to look baggy on him, France had to specially make all of them.
The actors playing the parents both previously appeared in films with a similar theme of suspended animation and revival. Mariette Hartley appeared in Genesis II (1973), about a man in suspended animation revived in the distant future after being buried by an earthquake; and Richard Masur appeared in The Thing (1982), as part of a team of scientists who revive a frozen, buried alien from the past.