The disseration deals with the creation of a mathematical model for the calculation of radial stiffnesses of slewing bearing with point contact. At the begining of this work is developed a theoretical part dealing with the basic division of bearing types. Subsequently, their functional parts are described. At the end of the theoretical part, the work deals with the way in which it is possible to solve the problem and also describes the basics used in the analytical solution of the problem. In the introduction to the part, the work dealt with the creation of a cirtual 3D model of slewing bearing. After creating a virtual model, the work was devoted to the preparation of structural finite element analyzes As the next step the values obtained by the FEM calculation were used to obtain the functional dependenes berween the introduced coefficient and the given dimensional parameters of the bearing. In the next stage, the values of the coefficient variables were optimized and a program code was also constructed to verify the calculated results. In the last part of the work, the procedure for derivation and calculation of radial stiffnesses in slewing bearing with point contact was described. At the end of the work there is an interview about possible benefits and results for practice.