A method and construction site device for vertical transportation during a building construction phase include a climbing formwork platform arranged in a currently uppermost region of the building for concreting at least part of the building core, an elevator car intermittently adjusted to a current building height in a first elevator shaft by hoisting a mechanical platform to a higher level and fixing it there, a construction elevator temporarily installed in a second elevator shaft and attached to the climbing formwork platform with a construction elevator car vertically movable in a construction elevator frame, and wherein people and/or material are transported to a floor associated with an access opening of the construction elevator by the elevator system and then are transported from this floor to a floor situated in the currently uppermost region of the building or to the climbing formwork platform by the construction elevator.