The results of the numerical analysis are convergent with the experimental studies in terms of both the solution of the eigenproblem and the kinematically excited vibration. The convergence of the results obtained was satisfactory, i.e. the average error between the frequencies obtained through classic modal analysis and the frequencies obtained numerically was only 5%. The dynamic response of the numerical model to the kinematic excitation was almost exactly the same as the real structure response in cases where only the horizontal component of the ground motion was taken into account. In cases where both components were taken into consideration, the extreme values of the amplitudes were the same. In the latter, the differences in the vibration character may have been caused by the geometrical imperfections of the real model or the imperfections in carrying out the measurements. The theoretical results were verified experimentally, thus proving that the theoretical analysis was carried out correctly. It may therefore be maintained that the phenomenon of parametric resonance is a real danger in tall buildings secured against the negative effects of earthquakes with a TMD in the form of pendulum.