What could be causing a Thump from the rear of the vehicle?

Hello, are you for certain it's coming from the rear? Is your Edge the All Wheel Drive version? Just a guess, but check mounts of the engine, transmission, subframe and if equipped - rear differential. But, really, you should have a technician near you evaluate the concern by showing him or her the noise and having them trace down the source of the concern. Use this link to find some shops near you that can help with your concern: www.repairpal.com/repair-shops