The report includes the updated results of analysis of buckling and vibrations of thin-walled structures previously reported in [1, 2]. Free vibrations of a thin plate with multiple cut-outs are modeled by means of analytic and numerical methods. The effect of the total area of holes, their positions and shapes, the shape of a plate shape and the plate side ratio on natural frequencies and modes of free vibrations is studied. It appeared that the natural frequencies may either increase or decrease with the total cut-outs area since the holes affects both the stiffness and the mass of a plate. The interaction between holes and modes of vibrations plays the crucial role. For small cutout area the asymptotic formula for natural frequencies has been obtained and the asymptotic results have been compared with the results of numerical analysis.