The topic of the thesis is "Analysis of the influence of properties of shape, geometry and materials on deformations and stresses in the work of expansion joints." The paper is divided into theoretical and analys part how equivalent stresses have effect on number of cycles before break. The theoretical part of the paper lists and describes the most important types of compensators and technologies that are most often used in the manufacture of compensator parts. Also, the most important materials used for the production of compensator parts are mentioned, with special emphasis on their chemical composition and the required mechanical, physical and technological properties. Also, the most important parameters that play an important role in the selection of materials for the manufacture of compensator parts, such as working medium, temperature and stress, are listed. Nowadays, in addition to various standards types of stainless steels which have similar mechanical properties, due to a number of advantages for the production of compensator parts, nickel alloys are increasingly used, such as Inconel, Monel and Hastelloy alloys. In analysis part is compered stresses and strains in the body of the compensator with number of cycles. Through the comparison on the selected standard bellows, the dependence between the axial displacement and the equivalent stress can be observed, in such a way that the increase in the axial displacement increases the total equivalent stress. Based on a matematical formula the number of cycles can theoretically be calculated at all values of the equivalent stress. At low values of the equivalent stress, large amounts of cycles are realized, which means that it is difficult to determine the exact number of cycles. With large values of the equivalent stress, smaller amounts of cycles are realized and thus the actualc and theoretical values are more accurate.