The statement of the problem and algorithm of computational modeling of the processes of formation of the hydrogen-air mixture in the atmosphere, its explosion (taking into account chemical interaction) and dispersion of the combustion materials in the open space with complex relief are presented. The finite-difference scheme was developed for the case of the three-dimensional system of gas dynamics equations complemented by the mass conservation laws of the gas admixture and combustion materials. The algorithm of the computation of thermal and physical parameters of the gas mixture appearing as a result of the instantaneous explosion taking into account chemical interaction was developed. The algorithm of computational solution of the difference scheme obtained on the basis of Godunov method was considered. The verification of the mathematical model showed its acceptable accuracy in comparison with known experimental data. It allows using the developed model for the modeling of pressure and thermal consequences of possible failures at the industrial enterprises which store and use hydrogen. The computational modeling of an explosion of the gas hydrogen cloud appearing as a result of instantaneous destruction of high pressure containers at the fueling station was carried out. The analysis of different ways of protection of the surrounding buildings from destructive effects of the shock wave was conducted. The recommendations considering the choice of dimensions of the protection area around the fuelling station were worked out.