I am a Rumble main, I'll tell you who I personally have the most trouble with:
Amumu: His range is similar to Rumbles, and he has a stun and can lower MR. I have lost every single time to amumu solo top as Rumble, he's a suprisingly good counter.
Volibear: Your passive regen > Rumble flamespitter damage in a 1v1 fight, plus you're guaranteed a kill with your toss during a gank.
These are the ONLY champs I'm not able to either kill or outfarm as Rumble. Keep in mind I'm not very high ELO though.
Don't pick Morde, he's pretty easy to beat unless Rumble is stupid enough to engage when his shield is up.
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