This work investigates the impact of deep coal mining induced vibrations on surface constructions using numerical tools. An experimental study of the geological site amplification and of its influence on mining induced vibrations has already been published in the previous paper (Part 1: Experimental evidence for site effects in a coal basin). Measurements have shown the existence of an amplification area in the southern part of the basin where drilling data have shown the presence of particularly fractured and soft stratigraphic units. The present study, using the boundary element method (BEM) in the frequency domain, first investigates canonical geological structures in order to get general results for various sites. The amplification level at the surface is given as a function of the shape of the basin and of the velocity contrast with the bedrock. Next, the particular coal basin previously studied experimentally (Driad-Lebeau et al. [1]) is modeled numerically by BEM. The amplification phenomena characterized numerically for the induced vibrations are found to be compatible with the experimental findings such as: amplification level, frequency range and location. Finally, the whole work was necessary to fully assess the propagation and amplification of mine induced vibrations. The numerical results quantifying amplification can also be used to study other coal basins or various types of alluvial sites.