Dogs and cats can eat grass. It can be normal behavior dogs are omnivores and require both meant and plant material to survive. Grass is a form of roughage, which aids dogs indigestion. It is also possible that when your dog eats grass, it tastes good to him. Cats can eat grass. Cats,unlike dogs, are carnivores. They do not need as much plant material in their diet as dogs do.However, pet stores do carry cat grass that many cats seem to enjoy. Just as in dogs, the grass aids in digestion and many even be tasty. Just because your pet eats grass it does not necessarily mean that he is sick. But, be very careful not to let your cat or dog eat grass that has been recently fertilized. Lawn and plant fertilizers can make your pet very sick.