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Q: About digging on furniture...I have a puppy that digs on the bed or the mat. How do I stop him?
A: Training a puppy to be a "civilized" member of your family involves showing the dog over and over which activities are allowed and which are not. Consistency is absolutely essential for success.
Now, that does not mean simply telling the puppy "no!" as the puppy will want to do any of a number of natural activities such as digging again. A firm no may stop a pup momentarily, by distracting it, but it really doesn't learn much from that.
You need to show the puppy alternative activities that are allowed -- and then praise the pup for doing those things. For example, stop the pup from digging on the bed by telling it "no!" followed by picking it up off the bed, putting it on the floor and asking the pup to do an action you've trained it to do, such as "sit." When the pup sits, praise the pup. Then introduce a chew toy and praise the pup when it chews on its own special toy. You are encouraging a positive activity that is also natural -- chewing.
Now, about a pup "digging" on its own bed or mat [if that's what you meant by mat]. This is a very natural activity -- digging a hole or nest to sleep in. I see no reason why you would want to stop this. A dog should be able to prepare its sleeping place. You may want to avoid expensive dog beds if your pup really loves to dig before sleeping.
See my Behavior and Language section for more tips on digging dogs.