Additive production processes are increasingly represented industrial production, especially in the aerospace industry, automotive industry, medicine, dentistry, mechanical engineering and others. The development of additive procedures achieves a shorter production time, reduces the amount of waste material, enables the production of parts of complicated geometry and reduces the need for conventional procedures in production, especially in dentistry. Selective laser melting - SLM is one of the processes of additive production used in the production of cobalt - chromium alloys, Co-Cr. Additively produced cobalt – chromium alloys, due to the convenience of mechanical properties, are used in biomedical purposes, especially for metallic structures of dental appliances. During the testing of the mechanical properties of Co-Cr alloy by static tensile test, the test specimen slips out of the jaws of the tear-off machine. Slipping prevents performance of the experiment and obtaining the corresponding results. The objective of this paper is to propose the design of the test specimen and the plate of the jaws of the tear-off machine in order to avoid slipping. The paper is divided into theoretical and experimental part. The theoretical part of the paper is about additive production, its historical development, production method, classification and comparison with conventional production methods. Selective laser melting - SLM as a type of additive production is then described in more detail. This chapter discusses the production process itself, the parameters of the process and its application. The theoretical part of the paper also describes the static tensile test and the equipment needed to perform it. In the experimental part of the paper, the reasons for the slip of the test specimen are described and the optimal solution for the design of the test specimen and the jaw plate is proposed.