How do you get inside Cerulean City Cave?

To get in the cave you have to defeat the Elite Four.

Return the Ruby and Sapphire to Celio and go to Cerulean City.

You have to do the league with at least 60 Pokemon in your Pokedex to get it Cerulean Cave.

After you beat the Elite Four the first time you:
1. Do that little deal with the gems for the Pokemon Machine for Celio in the 1,2,3 islands.
2. After the machine is fixed by Celio, you will be able to Trade for new Pokemon from anywhere on Ruby/Sapphire, Fire-red/Leaf-green with the Machine fixed, then battle the Elite Four a SECOND time and win.
(note: Elite Four will have stronger Pokemon, not to mention different)
Here are the Pokemon they will have 2nd time:
1. Lorelei's Pokemon:
| Dewgong | 64 |
Piloswine | 63 |
Cloyster | 63 |
Jynx | 66 |
Lapras | 66 |
2.Bruno's Pokemon:
| Steelix | 65 |
Steelix | 66 |
Hitmonchan | 65 |
Hitmonlee | 65 |
Machamp | 68 |
3.Agatha's Pokemon:
Gengar | 66 |
Misdreavus | 65 |
Crobat | 66 |
Arbok | 68 |
Gengar | 70 |
4.Lance's Pokemon:
Gyarados | 68 |
Aerodactyl | 70 |
Dragonite | 66 |
Dragonite | 72 |
Kingdra | 66 |
5.Gary's Pokemon:
Bulbasaur | Charmander | Squirtle | Which one's your Starter?
Heracross.....72 Heracross....72 Heracross....72
Tyranitar.......72 Tyranitar.....72 Tyranitar.......72
Gyarados.....73 Exeggutor....73 Arcanine.......73
Alakazam.....73 Alakazam.....73 Alakazam.....73
Exeggutor.....73 Arcanine.......73 Gyarados.....73
Charizard....75 Blastoise....75 Venusaur.....75

3.Voila, after beating them the SECOND time around, go to Cerulean Cave and you can now have access to find, and hopefully, capture Mewtwo, one of the most, probably THE most, powerful psychic Pokemon in the game.

You need to have beaten the Elite 4 twice and have all HM'S, well in order to beat the Elite 4 twice you need to get Lorelei back and that requires Waterfall.
Good luck, and make sure to use either the masterball or a LOT of ultra balls on Mewtwo.

First you have to get the Ruby and Sapphire

Give Celio the Ruby and Sapphire. This has NOTHING to do with the legendary dogs but beat the Elite Four first. I'm not so sure about that!

To get in that cave, you must have defeaten the Elite Four and conquer all the missions on island 1-7. (This includes beating Team Rocket)

Beat the elite 4 and become the champion, then, do the ice cave and you should be able to go to the Cerulean Cave.

Hi everybody. Sorry I've been gone so long. Anyway, you need to beat the E4 and do everything on the islands. P.S. I like your name (mostly because it's mine).

Every answer you heard is bogus so far. The REAL way is to beat the Elite Four ONCE! Then go to mount ember battle 2 rocket guys, go into the cave and get the Ruby, get out return 2 Celio then he'll give you rainbow pass. Go to servault canyon ( 7 island) go to Dotted Hole use Cut right in front of door get sappire a guy will steal it. Go to Five Island into the warehouse in the meadow, if you have the 2 passwords you can go in. The way 2 the scientist is kinda like silph co. Once you get to him, beat him he gives ya the sappire then go to one islind talk 2 celio he gets the sappire,too now you can Trade with ruby&sappire version. Go to Cerulean Cave no man is there then go inside. You need Strength, rok smash and Surf follow the path you find Mewtwo who is caught with a pokeball

You get the Ruby and Saphire.

If I remember correctly the man standing in the way is saying you don't have enough accomplishments,so beat the Elite Four(once or twice) hatch (i think 1 egg)and since I got the Ruby and Sapphire before I got into the cave,i think you need to do that too.hope I helped

Evil

First,you need to defeat the Elite 4.Then,Complete all the island quest.Then last,the man will move and now you can catch Mewtwo with a Master Ball,or a LOT of ultra balls.

Its not letting me battle the rockets on my.ember or Celio won't ask for help with machine I beat e4forgot stones when Bill picked me up don't know what to do

No-one has said the correct answer, so I will. The easiest way, and most ideal way to get into Cerulean Cave is this.. Beat the Elite Four ONCE(Not twice) then complete the Kanto Pokedex, finding 151 Pokemon or 150 then go to OAK, he will give you the National Dex. After that, just go to Cerulean Cave. He will be either gone, or moved outta the way.

Sorry for all other answers not being clear (PS: I know it's been over ten years since you asked this, but I had to answer )