The aim of the study is to show the results of complex shaking table experimental investigation focused on the response of two models of cylindrical steel tanks under mining tremors and moderate earthquakes, including the aspects of diagnosis of structural damage. Firstly, the impact and the sweep-sine tests have been carried out, so as to determine the dynamic properties of models filled with different levels of liquid. Then, the models have been subjected to seismic and paraseismic excitations. Finally, one fully filled structure has been tested after introducing two different types of damages, so as to verify the method of damage diagnosis. The results of the impact and the sweep-sine tests show that filling the models with liquid leads to substantial reduction in natural frequencies, due to gradually increasing overall mass. Moreover, the results of sweep-sine tests clearly indicate that the increase in the liquid level results in significant increase in the damping structural ratio, which is the effect of damping properties of liquid due to its sloshing. The results of seismic and paraseismic tests indicate that filling the tank with liquid leads initially to considerable reduction in values of acceleration (damping effect of liquid sloshing); however, beyond a certain level of water filling, this regularity is inverted and acceleration values increase (effect of increasing total mass of the structure). Moreover, comparison of the responses under mining tremors and moderate earthquakes indicate that the power amplification factor of the mining tremors may be larger than the seismic power amplification factor. Finally, the results of damage diagnosis of fully filled steel tank model indicate that the forms of the Fourier spectra, together with the frequency and power spectral density values, can be directly related to the specific type of structural damage. They show a decrease in the natural frequencies for the model with unscrewed support bolts (global type of damage), while cutting the welds (local type of damage) has resulted in significant increase in values of the power spectral density for higher vibration modes.