A CFD framework is developed for simulating the unsteady flow through the port of a side-burning solid rocket motor to capture the ‘longitudinal mode acoustic instability’. The flow is modeled as inviscid and axisymmetric, simulated by solving the Euler equations in ANSYS Fluent. Propellant gasification is modeled as mass inlet boundary condition and the mass flux is taken as a function of the static pressure at this boundary. Combustion-acoustic coupling in the linear phase is accounted for by a response function formulation in which the burn rate fluctuations is calculated as a product of frequency response and corresponding pressure perturbation amplitude in the frequency domain. This is shown to lead to an exponential growth of pressure perturbations in the initial phase as observed in actual motor firings. This then transitions into a limit cycle unlike the DC shift observed in experiments. By accounting for the extinction-re-ignition of propellant subject to high amplitude pressure oscillations known to lead to burn rates as high as ten times the mean value for a fraction of the wave time period transition to DC shift is captured – a propellant centric theory for this phenomenon as opposed to earlier ones based on steep fronted waves. © 2018 Combustion Institute. All Rights Reserved.