Abstract: A method and apparatus for the production of a workpiece of exact geometry and high surface quality, such as, for example, a forming tool, are disclosed. Preferably computer-controlled, the apparatus follows the method of the invention to produce the workpiece by radiation and compacting of nx successive layers of powdered starting material, each subsequent layer being formed on the uppermost surface of the previously formed layer. Following the radiation and compacting of each layer, at least one of the vertical lateral faces of the layer and of one or more underlying layers, all of which are surrounded by excess powdered starting material throughout the process, are mechanically finished, for example by a hobbing process or a peripheral grinding process.