An interaction of a detonation wave propagating in the cellular detonation mode with a cloud of inert particles is investigated numerically. The analysis of results allows the regimes of propagation of the heterogeneous plane Chapman Jouguet and cellular detonations and their suppression to be identified. The influence of various parameters of the inert cloud is demonstrated. The critical length of the cloud sufficient for detonation suppression is determined. It is shown that the disperse composition and the nonuniform distribution of particles in the cloud are important parameters affecting the detonation propagation mode. (C) 2015 Elsevier Ltd. All rights reserved.