A method of manufacturing a three-dimensional object by a layer-by-layer application and selective solidification of a building material by exposure to a radiation. A hollow body is arranged in a process chamber above a build area which hollow body substantially extends from the build area in a direction of an upper side of the wall of the process chamber. Gas is supplied to the process chamber in such a manner and gas is discharged from the process chamber in such a manner that a lower pressure exists in the region of the process chamber lying within the hollow body than in the region of the process chamber lying outside the hollow body.