Clamping a workpiece and placing it in a proper position for a tool used for the removal of particles is an important and necessary procedure during processing. The clamping itself has to ensure that the position of the workpiece is fixed during the entire processing using a force that must not result in any deformation. The repeatability of the process depending on the planned number of reps, and the rapid interchangeability of workpieces must be ensured to achieve the required efficiency of the procedure. The clamping devices are designed for this purpose. The design of a clamping device includes a good knowledge of production technology, machines, the permitted tolerance of the workpiece, and the material for its production. This paper defines a clamping device, presents its basic components and describes its role and importance in processing. It describes the classification of clamping devices according to their use, design, method of preparation, and method of receiving and clamping the workpieces. Each of these methods of clamping and receiving has certain advantages and disadvantages that should be taken into consideration when designing clamping devices. Defining the clamping methods for a workpiece involves determining the workpiece support and the direction and amount of clamping force, while keeping the safety of the workpiece in mind. In this paper, a clamping device that is part of an automated machine produced by SAS Strojogradnja d.d. Zadar is designed for processing radiator ribs.