The subject of this thesis is a numerical analysis of the spacer damper rubber joint stiffness. Spacers dampers are used to maintain the gap between the overhead transmission lines and for damping of Aeolian vibrations. The aim of this work is to calculate the stiffness constants of the spacer damper rubber joint with the ultimate goal of creating a correct numerical model that can display sufficiently accurate response to arbitrary dynamic excitation. Analysis was carried out numerically using the finite element method in commercial software packages of company Dassault Systèmes Abaqus 6.9-3 CAE and MSC.Software Corporation MSC SimDesigner R4 CATIA V5R18 WBE inside of Dassault Systèmes CATIA V5R18 SP3 P3 interface. The work is divided into nine sections. In the first, introductory section, the Aeolian vibration problem, with basic types and way of functioning of the spacer dampers are briefly described. The energy balance method with calculation methods and possible errors that occur are also described. In the second section, the problem of determining the stiffness characteristics and the measurements of the stiffness and damping of the rubber joint are clarified. The third section briefly describes the finite element method and 1D, 2D and 3D finite elements used in the scope of work. In the fourth section, the basic principles of continuum mechanics, incremental-iterative method, geometric nonlinearity, material nonlinearity, and general nonlinear contact problem are briefly described. In the fifth section, finite elements and methodologies for use in multiple nonlinear contact problems are verified and validated through six detailed examples. In the sixth section, the course of creating the calculation model, as well as a number of iterations, simplifications and assumptions in order to create a simpler and sufficiently accurate model for the calculation using the finite element method, is extensively described. In the seventh section, the adopted numerical calculation model is presented. Model is compared to reference experimental data and examined through convergence of the obtained numerical results. In the eighth section, the visual and tabulated results of rubber joint stiffness are shown. Also, a brief critical comparison of numerical design models created in software packages Abaqus and Nastran/Marc was made. In the ninth section, the comment was made on the results of the stiffness of the rubber joint. The necessity of checking numerical methods, both through many numerical formulation, and mandatory comparison with the experimental measurements was emphasized.