After you defeat the elite four, Raikou and Entei run around Johto. (Suicune can be captured in Kanto.)
Your first encounter with Raikou is completely by luck and chance, but once you see raikou once, you can keep track of what area it is in.
again, Raikou can be found in every route in Johto, but he changes location each time you enter a building, go to a different route, or enter a city.
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he roams the map after you beat the game
You cannot catch Raikou in Pokemon Diamond and Pearl. To get Raikou in Pokemon Diamond and Pearl, you must trade for one from Pokemon HeartGold and SoulSilver where it can be caught or transferring from Pokemon FireRed and LeafGreen.
raikou cannot be caught on Pokemon ruby
after that, someone at the battle frontier will tell you about latias and latios. then, latias will start roaming kanto.
Pokemon HeartGold and SoulSilver.