The method of the numerical solution of a three-dimensional problem of atmospheric release, dispersion and explosion of gaseous admixtures is presented. It can be equally applied for gases of different densities, including hydrogen. The system of simplified Navier-Stocks equations received by truncation of viscous members (Euler equations with source members) is used to obtain a numerical solution. The algorithm is based on explicit finite-difference Godunov scheme of arbitrary parameters breakup disintegration. To verify the developed model and computer system comparisons of numerical calculations with the published experimental data on dispersion of methane and hydrocarbons explosions have been carried out. Computational experiments on evaporation and dispersion of spilled liquid hydrogen and released gaseous hydrogen at different wind speeds have been conducted. The largest mass concentrations of hydrogen between bottom and top limits of flame propagation and cloud borders have been determined. The problem of explosion of hydrogen-air cloud of the complex form generated by large-scale spillage of liquid hydrogen and instant release of gaseous hydrogen has been numerically solved at low wind speed. Shock-wave loadings affecting the buildings located on distance of 52 m from a hydrogen release place have been shown.