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The first step is to understand what is causing the dog to constantly dig. Let your dog out and then observer their behavior from inside the home. As mentioned above it may be that the dog is simple bored and full of energy. In this situation you must exercise your dog on a daily basis. Long walks tiring the dog out are the best remedy for the bored dog. They will be so tired digging is the last thing on their mind.
This also applies to the dog that tries to dig under the fence. They need to get out and run! So do what needs doing, and exercise the pooch.
For those breeds like Terriers who instinctively dig more than other breeds, a good way to solve this is provide a place in the yard for them to dig to their hearts desire. Box in a square spot and fill with loose dirt. Now hide treats and favorite toys in the dirt while the dog is inside the home and cannot see what you are doing. When you let the dog out he will smell these items and go to this spot. This will become their dig area as long as you keep treats and toys buried there.
Use the dog’s desire to dig by following the above tips. You CAN stop your dog’s digging, or at least contain it with the right knowledge.