In the paper the physical and mathematical model for the description of the processes of transition, attenuation and suppression of detonation in hydrogen-air mixture in one- and two-dimensional formulation, taking into account reduced and detailed kinetics of chemical transformations in reactive gases, by inert gas plugs was proposed. On the basis of this model calculations of the interaction of plane (in one-dimensional formulation) and cellular (in two-dimensional formulation) detonation wave propagating in hydrogen-air mixture with layer of inert gases (argon, nitrogen, carbon dioxide) were performed. It was shown that depending on the type of isolating gas and the length of the plug various flow regimes were realized after the shock wave exits from the inert gas plug: a) reinitiation of detonation wave; b) suppression of the detonation wave with the formation of a deflagration wave at the end of the inert gas plug; c) suppression of the detonation wave with the combustion zone isolation by inert gas plug. The geometric limits of detonation (minimum inert gas plug length leads to detonation suppression with combustion zone isolation) for all three types of inert gas plugs were calculated. Comparison of the effectiveness of detonation suppression by various inert gas plugs shows that the carbon dioxide is more efficient for suppressing the detonation wave, i.e. geometric limits of detonation during interaction of detonation with carbon dioxide plug is smallest compared with other two types of plugs.