Like barking, digging is not a shepherd-specific trait. However, it is a behavior common among bored puppies. Again, the solution to this problem is more exercise, more interaction, more training, and less time alone — particularly outside where your pup or dog can dig.
There are some shepherds that will smell rodents underground and dig to get to them. Other puppies enjoy unearthing bulbs — many of which are poisonous when eaten — and shrubs. Some shepherds like to bury bones and then unearth them later. Older male puppies, those that have reached physical maturity, may dig under the fence in an attempt to reach a female in season; neutering solves this digging problem. In general, if you don't want your shepherd digging in the backyard, supervise her while she's outside. When she begins to dig, distract her with another activity for which you can praise her.
Keeping your dog occupied with activities will help eradicate unwanted behaviors.
If the location in which your puppy is digging is more of a problem than the fact that she is digging, block your puppy from that part of the yard. If you have a pup that enjoys burying her bones, you can select an area specifically for burying and digging up bones. To teach her that this is her digging space, choose a plot of about four by four feet, and bury a couple of bones in the ground. When the puppy digs and buries bones in the digging plot, praise her.
The digging plot requires that you supervise most of your puppy's activities in the yard to make sure she is praised for using the correct area of the yard. Over time, if your puppy has a treasure to bury, she will automatically go to her digging plot.