Spectral characteristics of the spherical elastic wave and the amplitude-frequency characteristics of the massive industrial explosions at the open-pit and underground mining of the coal deposits are studied in the article. It is shown that the removal of the spherical wave from the source moves the spectrum of vibrations to the low-frequency area. Frequency corresponding to the first mode of the oscillations in the spectrum does not depend on the number of single explosions in series, and the increase in the deceleration time in the series of explosions decreases the frequency of the fundamental harmonic. Based on the conducted studies, the recommendations are given on preserving the stability of the underground workings located near the places of massive industrial explosions at the open-cast coal mining. For example, as showed the studies of the spectral composition of mass industrial explosions, the wavelengths of the main harmonic of oscillations vary from 315 to 500 m and above. In this case, one should pay attention to the mine workings, the size of which is comparable with this wavelength. In the case, when the wavelength is two to three times bigger than the size of the workings, the mass industrial explosions will not effect their stability. In addition to this, to protect the workings, it is required to increase the time of deceleration of explosions in the series up to 60 ms and more, and, also the number of exploding wells in each series. In the cases where the size of the saved workings is compatible with the wavelength of the main harmonic or exceeds it, it is required to carry out additional fastening of the workings. Given recommendations do not contradict the conclusions made from the results of the field observations in the published works of various authors.