Any behavior changes such as excessive barking, howling, panting, running away etc. should be a warning sign for anxiety. You, as an owner, need to take care of your dog’s mental health. But if you are wondering how you are going to know whether your dog is anxious or not, well, you should look for the following symptoms in your dog, Barking or howling when you will not be close to it. Panting during not-so-hot and humid weather.  Shivering. Running away from you and even hiding when you are around. Digging on the ground. Destruction of objects around it. Causing self-harm.