Instructions
Go to Cianwood City and walk north until you reach a hill. Continue walking towards the top of the hill until you see Suicune. Approach him and press the "A" button; he will run away.
Proceed through the game until you arrive at Mt. Mortar. You will encounter Suicune once again at the entrance of Mt. Mortar, and again he will run away.
Continue through the game until you have defeated trainers in the Pokemon League in the Johto region to unlock the Kanto region. As you continue your journey into Vermillion City, Suicune will appear at the entrance of the city. For the third time, he will run away.
Take Route 14 and go towards Cerulean City, where you will see Suicune. He will run away for the fourth and final time. Enter Cerulean City and defeat the gym leader, Misty. Once you have obtained the badge, go towards Bill's House, which is located along Route 25.
Save the game before you reach Bill's House; you will encounter Suicune as soon as you step inside the front yard of the house. This time, he will stand his ground.
Battle Suicune with any type of Pokemon except Fire and Rock-type Pokemon, which are the only creatures that are weak against Suicune. Since Suicune is a Water-type Pokemon, Lightning and Plant-type Pokemon are strong against Suicune. To increase your chances of catching Suicune, hit him with an attack that produces paralyzing, freezing or sleeping effects.
Catch Suicune with any type of Poke Ball. Great Balls and Ultra Balls have a higher rate of success than regular Poke Balls, especially when it comes to catching higher level and stronger Pokemon. Once you have captured Suicune, he will be transferred to Bill's PC if you do not have room for Suicune in your current Pokemon party.