The article presents the results of simulation of coupled processes of rock deformation and liquid polymer filtration in the disturbed area around the mine working. The problem formulation takes into account the initial permeability of host rocks as well as the permeability due to the mine working driving, time of polymer delivery and hardening, and foaming effect of the polymeric composition in the process of mixing of its components. Certain changes in physicomechanical and filtration characteristics of rocks during the polymer hardening also were taken into account in the problem formulation as well as the fact that a metal delivery pipe starts operating as a reinforcing element after hardening of the polymeric composition is over. It was demonstrated that the location of rock bolts is important to form a rockbolts arch. With sufficient density of injection rock bolts, the formed rock-bolts arch may serve as a barrier controlling both water inflow and gas emission from the undermined rocks into the mine working. Dependence of changes in the reinforced area upon the value of initial permeability of the host rocks was derived. If the values of initial permeability are low then size of the rock-bolt supports and their shape are determined using only a value of the unloaded zone around the mine working. It was shown that steel and injection rock bolts complement each other very well, increasing the stability of the mine working and reducing the filtration permeability of the host rocks. Injection rock bolts exclude the possibility of destruction of host rocks and more effectively reduce the permeability of disturbed rocks in the zone of influence of the tectonic fault. And steel rock bolts better restrain the expansion of the zone of increased difference of the stress tensor components. Therefore, in the case of heavily watered rocks or a high probability of methane breakthroughs into the mine working, it is better to install injection rock bolts and deliver the polymer into the disturbed rock as close as possible to the mine face. Then a water- and gas-proof shell arch around the mine working will be created in the immediate vicinity of the mine face, which will make it possible to quickly prevent emergency water inflows and gas emissions. If there is no such threat and the priority is to maintain the long-term stability of the mine working, then first of all it is necessary to install steel rock bolts with polymer fixing in the borehole. Key words: injection rock bolts, complicated mining and geological conditions, numerical simulation, supporting technology, mine workings.