Process for producing an article comprising the steps of: I) depositing a free-radically crosslinked resin on a carrier to obtain a ply of a construction material joined to the carrier which corresponds to a first selected cross section of the article; II) depositing a free-radically crosslinked resin on a previously deposited ply of the construction material to obtain a further ply of the construction material which corresponds to a further selected cross section of the article and is joined to the previously applied ply; III) repeating step II) until the article has been formed; wherein the depositing of a free-radically crosslinked resin at least in step II) is carried out by illumination and/or irradiation of a selected region of a free-radically crosslinkable resin according to the particular selected cross section of the article, wherein the carrier is arranged inside a container and the container contains the free-radically crosslinkable resin and a liquid immiscible with the free-radically crosslinkable resin which has a higher density than the free-radically crosslinkable resin, thus causing the free-radically crosslinkable resin to float on the liquid and wherein before each step II) the distance between the carrier and the free-radically crosslinkable resin is altered such that a layer of the free-radically crosslinkable resin forms above the vertically uppermost surface of the previously deposited ply of the construction material and at least partially contacts this uppermost surface of the previously deposited ply of the construction material, wherein the free-radically crosslinkable resin comprises a urethane (meth)acrylate, characterized in that the free-radically crosslinkable resin comprises at least one isocyanate-functional compound which comprises at least one radiation-curable group selected from vinyl, propenyl, allyl, vinyl ether, maleyl, fumaryl, maleimide, dicyclopentadienyl, acrylamide and (meth)acrylate groups or a combination of at least two of these (component A) and comprises at least one NCO-reactive compound (component B). I) depositing a free-radically crosslinked resin on a carrier to obtain a ply of a construction material joined to the carrier which corresponds to a first selected cross section of the article; II) depositing a free-radically crosslinked resin on a previously deposited ply of the construction material to obtain a further ply of the construction material which corresponds to a further selected cross section of the article and is joined to the previously applied ply; III) repeating step II) until the article has been formed; wherein the depositing of a free-radically crosslinked resin at least in step II) is carried out by illumination and/or irradiation of a selected region of a free-radically crosslinkable resin according to the particular selected cross section of the article, wherein the carrier is arranged inside a container and the container contains the free-radically crosslinkable resin and a liquid immiscible with the free-radically crosslinkable resin which has a higher density than the free-radically crosslinkable resin, thus causing the free-radically crosslinkable resin to float on the liquid and wherein before each step II) the distance between the carrier and the free-radically crosslinkable resin is altered such that a layer of the free-radically crosslinkable resin forms above the vertically uppermost surface of the previously deposited ply of the construction material and at least partially contacts this uppermost surface of the previously deposited ply of the construction material, wherein the free-radically crosslinkable resin comprises a urethane (meth)acrylate, characterized in that the free-radically crosslinkable resin comprises at least one isocyanate-functional compound which comprises at least one radiation-curable group selected from vinyl, propenyl, allyl, vinyl ether, maleyl, fumaryl, maleimide, dicyclopentadienyl, acrylamide and (meth)acrylate groups or a combination of at least two of these (component A) and comprises at least one NCO-reactive compound (component B).