Flat Cats are a species of non-sapient Martian animals described in Robert A. Heinlein's science fiction novel The Rolling Stones.
In the chapter "Free Enterprise", the character Mr. Angelo, a shopkeeper on Mars, introduces Castor and Pollux Stone to a flat cat:
"Angelo tickled it with a forefinger; it began to purr like a high-pitched buzzer. It had no discernible features, being merely a pie-shaped mass of sleek red fur a little darker than Castor's own hair. "They're affectionate little things and many of the sand rats keep them for pets - a man has to have someone to talk to when he's out prospecting and a flat cat is better than a wife because it can't talk back. It just purrs and snuggles up to you."
The boys take the flat cat onto the family space ship, where it soon has eight "kittens", each of which soon gives birth again, until the ship is overwhelmed with flat cats. The family solves the problem by rounding up the flat cats and putting them into the storage hold at low temperature, where they hibernate. They are later revived and sold to miners in the asteroid belt.
Heinlein's flat cats are often said to have been the inspiration for The Trouble with Tribbles, an episode of the Star Trek television series. David Gerrold, the author of the Star Trek episode, claims that he was not familiar with the Heinlein novel when he wrote the screenplay; when he found out the two stories were similar he asked Heinlein for permission to use the idea, which Heinlein granted in exchange for an autographed copy of the script.