A three-dimensional mathematical model of gaseous hydrogen deflagration in the enclosed space is developed. The process is described by the system of gas dynamics differential equations. Thermodynamic parameters of the mixture and its components are defined as functions of the local temperature and mixture composition. The concentration changes of the fuel and combustion products are determined using conservation laws taking into account rates of component disappearance and formation and turbulent diffusion. It is assumed, that the chemical reaction takes place only in the volume where the fuel concentration is within the limits of inflammability. The mathematical model is validated during an intercomparison test to predict deflagration of a large-scale hydrogen-air mixture in open atmosphere. An algorithm of numerical solution based on the Godunov method is developed. A computer system of engineering analysis of gas-dynamic processes of hydrogen-air mixture formation and combustion in enclosed space with natural ventilation is created. It allows predicting the history of the changes of overpressure, temperature, concentrations of hydrogen and combustion products and other thermogas- dynamic parameters of the mixture in space. This prognosis can be used to estimate dangerous zones of destruction and recommend some safety measures.