Animal rights activists and actor Robert Culp filed the lawsuit in August 2007.
The suit alleges that the zoo is guilty of animal abuse and that the $42 million exhibit is a waste of taxpayer money because it is too small for the three elephants.
Culp has since died.
The case was dismissed and then an appellate court sent it back for trial.
The exhibit opens Dec. 16.
The Associated Press contributed to this report.