The events of multiple neutron production under 2000g/cm$^2$ thick rock absorber were studied at the Tien~Shan mountain cosmic ray station, at the altitude of 3340m above the sea level. From comparison of the experimental and Geant4 simulated neutron multiplicity spectra it follows that the great bulk of these events can be explained by interaction of cosmic ray muons with internal material of the neutron detector. In synchronous operation of the underground neutron monitor with the Tien~Shan shower detector system it was found that the characteristics of the muonic component of extensive air showers which is seemingly responsible for generation of the neutron events underground do change noticeably within the energy range of the knee of primary cosmic ray spectrum. Some peculiar shower events were detected when the neutron signal reveals itself only $sim$(100--1000),$mu$s after the passage of the shower particles front which probably means an existence of corresponding delay of the muon flux in such events.
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