It's not a thick cover, it has no padding, just a polyester fabric that covers the amp. The fit is quite tight.
The cover is folded when you recieve it, you can use an steaming iron on a low setting to remove the wrinkles if you want to. (do not use high setting, the black paint probably will stick on your iron)
Rocketbass amps are not super easy to scratch, but when you do, the 'tolex' tears open when you scratch them. You can not polish that scratch away.. ;-) So, i highly recommand to use this cover during transport!