Sometimes rust is like a bad tattoo—you need professional help. If the stains are deep or the drum is actually corroded, you might need to replace the machine. But before you call a repair guy, try a commercial rust remover like CLR or Whink.
Follow the instructions exactly—these chemicals are not for eating, sniffing, or using near your pet iguana. I once used a shop-vac to suck out leftover remover water and felt like a laundry ninja.
How to More Easily Remove Rust from your Clothes Washer Lid - YouTube