Is eating grass normal or abnormal for your pet ??

Since we live in the country side I think my dog kind of got used to eat grass constantly and that's the reason she keeps eating it, haha! The only problem is that even when she likes to eat it, grass makes her sick apparently. She always throws up when she has been picking some roots up from the ground, so I always have to run after her so she wouldn't be throwing up constantly. It's kind of sad tho be honest, it seems like she really enjoys it and I wouldn't say that grass is that bad for animals. Her stomach can't take hay either - we have plenty of that around us constantly, so she has been trying to taste it too. That's the only thing I consider not being good for her since it can sometimes be too bad for horses too, if consumed large amounts per day.