The results of numerical modeling of intense shock wave propagation after explosion in a mine opening with permeable screen are presented. The problem is solved in the equilibrium non-viscous formulation without regard to chemical reactions and with averaged composition of mine air. It is shown that for a screen composed of four similar permeable barriers arranged as a labyrinth, the incoming shock wave has a strongest impact on the first barrier. As a consequence of weakening of the shock wave front on the first barrier, the rest barriers experience much less loading. In order to decrease peak loads on a load-bearing frame, it is necessary to reduce areas of flat front surfaces of metal structures.