There are two tabs that sit underneath the sides of the face plate. They have a tendency to break out the plastic over top of them while removing the covers. To help prevent this, push inward on the side of the cover, just behind the face plate as you take off the covers.

Lift up on the rear of the top cover, and slide it towards the back of the radio to disengage the three tabs at the front.

Repeat for the bottom cover of the radio.