Box Elder County is a county located in the U.S. state of Utah. As of the 2010 Census, the population was 49,975. Its county seat and largest city is Brigham City. The county was named for the box elder trees with which the county abounds.Box Elder County lies on the north end of the Great Salt Lake, covering a large area north to the Idaho border and west to the Nevada border. Included in this area are large tracts of barren desert, contrasted by high, forested mountains.