Climbing is completely prohibited!
Update 08/2023: Based on The Finnish Heritage Agency (Museovirasto) all climbing in Suomenlinna area is forbidden. This is due to the potential damage it might cause to the historical buildings.
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You can reach the crag with the HSL ferry from Kauppatori. If you come by car you leave it to Kauppatori where are only a few park spots. The nearby area has more. Walk from the Suomenlinna harbor to Susisaari and follow the map.
Keep in mind that the place is a cultural treasure. So when you leave, take everything that you brought, do not litter, don't keep too much noise or climb the built walls. Respect others how are enjoying the beautiful island and most important respect the plants and the animals, even the smallest ones. They were there before you.
Follow the general rules of Suomenlinna:
https://www.suomenlinna.fi/kavijalle/saannot-ja-ohjeet/jarjestyssaannot/
https://www.suomenlinna.fi/en/visitor/regulations-and-instructions/regulations/