The method of the numerical solution of a three-dimensional problem of atmospheric release, dispersion andexplosion 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 viscousmembers (Euler equations with source members) is used to obtain a numerical solution. The algorithm isbased on explicit finite-difference Godunov scheme of arbitrary parameters breakup disintegration. To verifythe developed model and computer system comparisons of numerical calculations with the publishedexperimental data on dispersion of methane and hydrocarbons explosions have been carried out.Computational experiments on evaporation and dispersion of spilled liquid hydrogen and released gaseoushydrogen at different wind speeds have been conducted. The largest mass concentrations of hydrogenbetween bottom and top limits of flame propagation and cloud borders have been determined. The problemof explosion of hydrogen-air cloud of the complex form generated by large-scale spillage of liquid hydrogenand instant release of gaseous hydrogen has been numerically solved at low wind speed. Shock-waveloadings affecting the buildings located on distance of 52 m from a hydrogen release place have been shown.