The invention relates to a device for producing three-dimensional workpieces, The device comprises a carrier for receiving raw material powder and a radiation unit for selectively radiating the raw material powder applied to the carrier with electromagnetic radiation or particle radiation in order to produce on the carrier a workpiece made of the raw material powder by a generative layering construction process. The device also comprises a vertical movement means, which is designed to move the radiation unit vertically relative to the carrier, and a cylinder construction wall, which extends substantially vertically and which constitutes a lateral delimitation for the raw material powder applied to the carrier, wherein the cylinder construction wall is designed to increase its vertical height during the construction process.