One building on George Square has a large sign proclaiming it is a “United States Court House” with the Stars and Stripes flying above the door.
Fans have been out in force hoping for a glimpse of Brad, and have been gathering at barriers placed at the entrance to the set.
He and his family arrived in Glasgow by train on Tuesday along with other cast and crew.
The film is based on Max Brooks’ 2006 novel World War Z: An Oral History Of The Zombie War, which is set in Philadelphia in the aftermath of a war between humans and zombies. It is due to be released next year.
Glasgow City Council said the production will involve almost 1,200 people when on location and the impact on the local economy is likely to be in excess of £2 million.