Abstract: A transient burning model of solid propellants is proposed,in which the distributed reactions and deep absorption of external radiation are considered in the condensed phase.The heat loss due to boiling heat transfer induced by liquid jet impinged on burning surface is taken into consideration in the energy balance equation on the buring surface.A space wise thick flame model is developed to obtain the flame heat feedback under the conditions that the decreasing of chamber pressure and gas phase temperatures is caused by liquid injection and evaporation of liquid drops in gas phase,which is described by a submodel for internal ballistics of rocket motor durning liquid quench.The model can be used to describe the transient burning behaviors of solid propellants under the influence of external disturbances,such as rapid depressurization,deradiation or liquid injection,and to obtain the critical values required for extinction of solid propellants.The results from theoretical prediction indicate that whether the transient burning comes into extinction is not only dependent on the variation rate of the external disturbance,but also on the variation amplitude of the disturbance.The critical values of liquid injection pressure drops for extinction of two kinds of aluminized ammonium perchlorate hydroxyterminated polybutadiene propellants(16%Al and 18 5%Al)were obtained by experiments.The predicted results obtained from the transient burning model are in good agreement with the experimental data.The critical value of liquid injection pressure drop increases with increasing propellant energy and chamber pressure.