The subject of this master thesis is to create a simplified discretised numerical model, appropriate for the calculation of axial vibrations in transformer windings. The content of the thesis introduction is theory required for understanding the issues that are being tackled. Transformer description gives an insight in the transformer construction and in the terminology that is being used. Theory of vibration gives an insight in the physics of the problem. A short description of the finite elements that were used is also given. A detailed description of the transformer components is given in the chapter that follows the introduction. The mentioned power transformer was designed by the company Končar Energetski Transformatori. The detailed description includes part dimensions, material properties and part positions. Necessary modifications of material properties and part dimensions are listed and described. The modifications were introduced in order to simplify the complex transformer structures or to avoid possible numerical difficulties. This is followed by numerical model descriptions. The detailed numerical model was prepared for the analysis in ANSYS, a finite element method based software. All the necessary steps in ANSYS are listed and described. The mathematically simpler numerical model was prepared for the analysis in MATLAB, a programming language that allows matrix manipulations. Matrix generation logic and matrix content is described. Numerical model descriptions are then followed by the results and the results comparison. In order to verify the simpler numerical model, results are first compared for the individual parts and for one assembly. The analysis have shown that the simple model yields good solutions for the eigenfrequencies calculations. The results off the entire transformer analysis are presented in the last chapter of the paper.