A one-dimensional mathematical approach is proposed to study gaseous flame reactions in the presence of reactive particles. The non-stationary model is based on the reactive Navier-Stokes equations for the gas phase, and on the reactive Euler equations for the particle phase, both phases being modeled as continua. The flux terms were treated by flux difference splitting schemes. Calculations were performed for a confined stoichiometric hydrogen/oxygen mixture enriched with carbonaceous particles and ignited y a temperature non-uniformity. The results show that the presence of particles has a damping influence on the ignition-induced pressure wave. The peak pressure and its propagation velocity decrease, and the sharp contour of the pressure wave is smeared out compared to the particle-free case. The increase of the temperature in the reaction zone is reduced due to heat absorption in case of non-reacting particles. With increasing particle reactivity, the equilibrium temperature is achieved earlier and the temperature level increases.