Modal analysis is the main topic of the thesis. First, the phenomenon of undamped oscillation is defined and concepts of modal coordinates and orthogonality of mode shapes which are crucial to the process of modal analysis are introduced. Various methods of applying load are presented: forced time-variable load, seismic load defined by ground accelerations and seismic load defined by response spectra. Methods for determining internal forces and displacements are shown along with ways of combining them. Next chapter contains a numerical example of a simple one-storey structure with three degrees of freedom analyzed with the method of modal analysis (using an acceleration response spectrum). Results are then verified in SAP2000. In the last chapter an eight-storey reinforced concrete building is analyzed with SAP2000. Vibration periods and internal forces in the element resisting the largest load are presented.