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Vortex-induced vibrations (VIV) is a phenomenon of self-exciting oscillations of elastic, or elastically mounted rigid bluff bodies exposed to in a gas or fluid flow. This sort of oscillations can be used to harvest electric energy from the kinetic energy of air or water flow. This fact determines the great practical significance in the study of this phenomenon. In this work, an experimental study of resonant self-exciting oscillations of a circular cylinder on a transverse flexible beam was carried out. In contrast to similar works with a similar configuration of the model that performs transverse translational oscillations, was discovered previously unexplored VIV type in which the cylinder rotates around the cantilever support. Experiments were performed in the Institute of Mechanics of Lomonosov Moscow State University in a wind tunnel A-10 with an Eiffel chamber and an open test section. To minimize the influence of the massive support, beam length was chosen in such a way that its length rated to the cylinder diameter was not less than 5. The beam with a 3×33 mm cross section was made of steel with density ρ = 7850 kg/m^3, Young’s modulus E = 224×10^9 Pa and Shear modulus G = 82×10^9 Pa. Cylinder was made of duralumin with mass mcyl = 0.116 kg, length L = 500 mm, external diameter 25 mm and internal diameter 23 mm. As expected, we observed classical quasi-two-dimensional VIV, at which the cylinder support experienced bending oscillations. However, we discovered a new type of VIV, which is caused by resonance of the vortex street with the torsional mode. During these fully three-dimensional torsional oscillations, von Karman vortex street, generated by upper and lower pieces of the cylinder, are shifted in phase by π. The Reynolds number range based on cylinder external diameter corresponding to the response region was (2.5–9.5)×10^3. In the present experiments, the maximum oscillation amplitude A/Dext = 0.34 was obtained. For a torsional resonance state, observed here for the first time, the characteristic reduced velocity range is 6..7.2, which corresponds to Strouhal number 0.166..0.139, which is explained by the finite span of the cylinder. The amplitude of torsional oscillations is investigated and turned out to be more than twice as large as of classical quasi-two-dimensional VIV, which suggests more effective energy harvesting from the torsional oscillations.