Travertine tile floors are generally not a good choice if you have pets in the house. As far as the durability goes, the tile can withstand pets running on it. In fact, the claws of the animal should not scratch the travertine tile at all. However, the big problem with putting pets on travertine tile floors is the urine. If the animal goes to the bathroom on the floor even once, the acid in the urine can etch the tile. Even if you clean it up immediately, the acid can still etch a permanent spot.