The biggest problem with removing dried paint from brick is getting out the last bits that stubbornly stick in the crevices. There are numerous products available for removing paint, but only a few basic methods. Which method you use to remove dried paint from brick will depend on the type of paint stain and how much elbow grease you're willing to invest.
Use a power washer. If you don't own one, your can rent one at many hardware stores and home centers.
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Hire a professional to sandblast the brick. If your brick is old or brittle it will probably be damaged by the process, so use it only if all else fails and you can't live with the dried paint.
Spray WD-40 on the paint. Wipe it up and repeat if necessary. Use a stiff brush to scrub any stubborn spots.
Buy a graffiti remover, such as Taginator or Graffiti Buster, designed specifically for masonry surfaces. Follow the manufacturer's instructions.
Use a sodium hydroxide stripper such as Peel Away. This kind of stripper works on both oil and latex paint spots, but it requires extra steps because it must be flushed from the surface and then neutralized.
Remove deeply embedded paint with a paste made from TSP and naptha. Spread it on, let it sit for a few minutes, then scrub.
Spread commercially available paint removers on the spots. Buy a remover that's designed to work on the type of paint stain you have, either oil or latex. Follow the manufacturer's directions.
Rinse the bricks completely with clean water once the paint has been removed.