After you encountering it in the wild, make sure you have a Pokemon with the Arena Trap/Shadow Tag ability or with the move Mean Look with enough speed to go first. Use Mean Look, if you do not have any of the listed abilities, then bring its HP at least yellow that is near the red. Now switch your Pokemon to make it paralyze or fall asleep with moves like Sleep Powder, Yawn, and Hypnosis. The catch rate has improved and it is time to try out an Ultra Ball. If you are playing Pokemon FireRed and LeafGreen, Timer Balls should be available to purchase, which are really convenient for legendary battles, for they take a lot longer than normal Pokemon. After about 5 failed throws from the Ultra Balls, throw a Timer Ball. Ensure it stays asleep or it can use Roar. In LeafGreen and FireRed, there's a fatal glitch where Raikou and Entei can disappear after using Roar. Eventually repeat the process to catch it easier. It can be the same way with Pokemon Gold, Silver, and Crystal, but Timer Balls were not purchasable at that time and Roar had no glitches, too.
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Use a fast ball or get a Pokemon with the move Mean Look so Raikou can't escape from battle. Have a magical day!
Using a master ball
raikou cannot be caught on Pokemon ruby
get a yoshi!
The same way you would catch a normal Pokemon. The only difference is is that the Pokemon is shiny.