There’s no reason why you can’t put a shed next to your fence or at the side of your house, but it’s important to consider maintenance and repairs to both structures. If your fence needs repair in the future, having the shed in the way will provide a limited amount of space to work. It’s typically easier to keep these structures at least a few yards away from one another so you have room to mow, paint, or fix one without the risk of damaging the other..