The legendary dogs are the hardest Pokémon to catch in FRLG. Which one you get is determined by your starter choice — and they flee on the first turn every time.
Roaming Pokémon use Roar or simply flee on turn 1. You almost never get more than one action before they escape.
They appear randomly in any tall grass in Kanto. Every time you change routes, they move to a new random location.
After your first encounter, open the Pokédex entry for the dog — the Area page shows its current location on the map.
Any damage or status condition (sleep, paralysis) you inflict carries over between encounters. This is key to catching them.
Unlock requirement: The legendary dog doesn't appear until you complete the main Sevii Islands storyline and receive the National Pokédex (requires seeing 60 Pokémon). Complete the game first.
Beat the Elite Four, then complete the Sevii Islands main quest (deliver the Sapphire stone to Celio on One Island). Professor Oak upgrades your Pokédex to the National Dex. The roaming dog activates immediately after this.
Walk through tall grass in different areas of Kanto until you randomly encounter your legendary dog. It will immediately flee — that's fine. You just need this first sighting to register it in your Pokédex.
This is the most important step. You need a Pokémon with Mean Look or Block (prevents fleeing) AND a Pokémon with a reliable sleep move. The two most effective catching Pokémon are:
Check the Pokédex to find which route the dog is on. Travel there and use a Max Repel. With Repel active, only Pokémon higher level than your lead Pokémon will appear — but the legendary dog (Lv. 50) will still force-encounter if you're lower level. Walk back and forth in the grass until it appears.
When the dog appears — act fast. On turn 1, use Mean Look or Block to prevent it from fleeing. The dog is now trapped. Then on subsequent turns, use Hypnosis or Spore to put it to sleep. Chip its HP down with weak moves, then start throwing Ultra Balls.
If the dog wakes up and you can't sleep it again before it flees — don't panic. The HP damage carries over! Keep hunting it, use Mean Look again next encounter, re-apply sleep, and throw more balls. Eventually it will be at low enough HP for a reliable catch.
Master Ball recommendation: The legendary dogs are the #1 best use of your Master Ball in FRLG. They are genuinely the hardest Pokémon in the game to catch due to the flee mechanic. If you don't want to spend hours hunting, use your Master Ball here — no shame in it.
Paralysis works too! You can't inflict paralysis AND sleep at the same time — but paralysis alone significantly increases catch rate and slows the dog. If you don't have a sleep move, a Pokémon with Thunder Wave + Mean Look will get the job done with enough Ultra Balls.