Abstract. It has been demonstrated in previous studies that local elastomer coatings covering the end coils of helical springs can efficiently reduce the amplitudes of circum-resonant vibrations in such springs. The analysis of the influence that elastic coatings have on the frequencies and modes of natural transverse vibrations of springs is presented in this paper. The concept of the equivalent beam of the Timoshenko type is utilized in calculations of the frequencies and modes of transverse vibrations. The model developed allows users to determine the frequencies and modes of symmetric as well as antisymmetric vibrations of axially loaded springs with elastic coatings of arbitrary length. A comparison of the results obtained using FEM analysis, in which the model represented the actual spring geometry, with the results obtained by means of the presented model indicates its high accuracy. model of a spatially curved rod, the model of an equivalent rod or beam, and the model in which a continuous system, such as a spring, is substituted by a discrete-periodic system consisting of concentrated masses joined by a mass-less stiffness, jointly representing one spring coil or its fragment. Equations of motion are written for an elementary fragment of a spring wire in the first model. Such a formulation of the problem [12, 13] allows arbitrary modes and frequencies of spring vibrations to be determined, however, solving it by analytical methods is very difficult and therefore such a solution is not suitable in practical applications. These difficulties mean that in several studies concerning the analysis of spring vibrations treated as a spatially curved rod, the authors use numerical methods. New finite elements, capable of modeling spring coils or their fragments were proposed in [14]. They are suitable for application in static problems as well as when looking for natural frequencies of helical springs. Mottershead provided, in the above-mentioned paper, experimental results later utilized by other authors. A similar approach to the problems of helical springs was presented in [15][16][17]. Pearson expanded -in [18] -equations provided by Wittrick [13], taking into account the influence of a static axial force. For determining natural vibrations, he applied the transfer matrix method. The same method was used in [19], concerning the analysis of parameters influencing natural frequencies of helical springs (utilizing the Cayley-Hamilton theorem), and in [20]. In this last paper, the authors compared their results with the results obtained on the basis of the Haringx model [21]. They pointed out that, in the case of helical springs with geometrical parameters, typical of springs used in machine buildings, the conformity between the results obtained by them and the results obtained using the Haringx model is high. In the numerical example quoted by them, for which the first 16 natural frequencies were determined, the maximum difference between their results and the ones from the Haringx model did not exceed 1.3%. In ...