The physical and mathematical models describing the detonation processes in hydrogen-air mixture in one- and two-dimensional formulation based on the detailed and reduced kinetics models were proposed. Using these models the interaction of a plane and cellular detonation waves with a semi-infinite cloud of inert particles was calculated. Types of detonation flows in the gas suspension in both detailed and reduced kinetics calculations were revealed. Volume concentrations and corresponding particle diameters resulting to detonation wave failure were obtained. Comparison of one-dimensional and two-dimensional approaches showed a quantitative similarity of the integral dependences of the normalized detonation wave velocity and the values of volume fraction and particle diameters at which detonation failure is occurs.