In this article, solid fuel transient burning behavior under oxidizer gas flow is numerically investigated. It is accomplished by the analysis of regression rate responses to the imposed sudden and oscillatory variations at inflow properties. The conjugate problem is considered by simultaneous solution of flow and solid-phase governing equations to compute the fuel regression rate. The advection upstream splitting method is used as the flow computational scheme in a finite volume method. The ignition phase is completely simulated to obtain the exact initial condition for response analysis. The results show that the transient burning effects that lead to the combustion instabilities and intermittent extinctions could be observed in solid fuels such as solid propellants.