RE: Is eating grass normal or abnormal for your pet ??
I don't know about dogs but cats love to chew on grass. That's the first thing they go to when I let them out during the day, the next stop being rolling in the gravel. This is why many pet owners, particularly those who don't live in a place where they can let their cats outdoors, grow or provide grass for their cats. I do that for them sometimes during the winter. There are cat grasses that you can grow for your cat which are more attractive to the cat, and more digestible.
Cats also eat grass (and sometimes other plants) in order to make themselves vomit, since they don't have fingers that they can put down their throats. Actually, this might be a means of purging themselves of hairballs, which is where we get the idea that it's not good for them.
Grass also satisfy the cat's need for fiber and roughage, as well as some different vitamins and minerals than they are getting through their regular diet, so there are a few reasons why cats might like to graze on the greenery. Cats usually know what's good for them and what isn't but a cat that is indoors all the time might not be able to make that distinction instinctively, so it's a good idea to keep any houseplants that might be bad for your cat out of its reach, since some of them can be toxic. Special grasses, such as those available in pet stores or online, might be a good idea for indoor cats.
Oat, wheat, and rye are good grasses for cats, and dogs like them too. These cereal grasses supply chlorophyll, amino acids, and minerals like potassium, calcium and magnesium, as well as vitamins, enzymes and protein, and can serve for detoxification, to correct nutritional deficiencies which you cat may instinctively be aware of, and to help with pancreatitis, digestive problems, skin and coat conditions, anemia, and respiratory problems. Cereal grasses can also improve the animal's breath and body odor. Barley grass is high in Vitamin B. Grass that has been cut up or minced is less likely to cause vomiting. Of course, that would reduce its efficacy in hairball removal.