Method of manufacturing a three-dimensional object by layer-by-layer application and selective solidification of a building material, comprising the steps of: applying a layer of the building material to a build area in a process chamber, selectively solidifying those positions of the applied layer which correspond to the cross-section of the object in this layer, by exposure to a radiation, and repeating the steps of applying and selectively solidifying until the three-dimensional object is completed, wherein a hollow body is arranged in the process chamber above the build area, which hollow body extends substantially from the build area in a direction towards the upper side of the wall of the process chamber, characterized in that 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, wherein a gas pressure is applied to the region of the process chamber lying outside the hollow body that is greater than or equal to the pressure outside the process chamber and wherein due to the lower pressure within the hollow body, gas flows from the region of the process chamber lying outside the hollow body through a gap between the build area and the lower side of the hollow body into the region of the process chamber lying within the hollow body and/or wherein due to the lower pressure within the hollow body, gas flows from the region of the process chamber lying outside the hollow body through a gap between the upper side of the wall of the process chamber and the upper side of the hollow body into the region of the process chamber lying within the hollow body. applying a layer of the building material to a build area in a process chamber, selectively solidifying those positions of the applied layer which correspond to the cross-section of the object in this layer, by exposure to a radiation, and repeating the steps of applying and selectively solidifying until the three-dimensional object is completed, wherein a hollow body is arranged in the process chamber above the build area, which hollow body extends substantially from the build area in a direction towards the upper side of the wall of the process chamber, characterized in that 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, wherein a gas pressure is applied to the region of the process chamber lying outside the hollow body that is greater than or equal to the pressure outside the process chamber and wherein due to the lower pressure within the hollow body, gas flows from the region of the process chamber lying outside the hollow body through a gap between the build area and the lower side of the hollow body into the region of the process chamber lying within the hollow body and/or wherein due to the lower pressure within the hollow body, gas flows from the region of the process chamber lying outside the hollow body through a gap between the upper side of the wall of the process chamber and the upper side of the hollow body into the region of the process chamber lying within the hollow body.