Convective combustion of mono-fuel aero-suspensions in an open-closed channel are treated numerically. The general approach to the problem of the simulation of the dispersed material behaviour to be exploited here is based upon incorporation of multiphase flow equations. The Lax-Wendroff two-step method is used for a solution of two-dimensional planar unsteady problems. The effect of acoustic oscillations caused by combustion upon combustion itself is studied. The different regimes (accelerated and decelerated– of convective combustion spreading are identified and the constitutive criterion of the realization of those regimes is suggested. The computational results to be obtained further are compared with available experimental data.