The objective of this study was to simulate the flame spreading and combustion processes in the ignition cartridge of a 120-mm mortar propulsion system under realistic firing conditions for performance improvements. In this work, theoretical modeling, numerical technique, and results of numerical simulation of the interior ballistic processes in the M1020 ignition cartridge of a 120-mm mortar system are presented. Modeling and simulation of the combustion processes in the granular propellant bed loaded with M48 ball propellants involves the solution of six coupled quasi-linear inhomogeneous hyperbolic partial differential equations (PDEs). These equations were formulated by applying the principles of conservation of mass, momentum and energy for condensed phase and gas phase in the granular propellant bed. In order to solve these equations for quantities of interest (i.e. pressure, propellant surface temperature, gas temperature, porosity, gas velocity, and propellant particle velocity), they were first converted to a system of ordinary differential equations (ODEs) using the method of characteristics (MOC). The MOC approach was selected because it introduces minimum numerical errors in converting the original system of PDEs into an equivalent system of ODEs. Calculated pressure-time traces showed axial pressure wave phenomena and compared closely with the measured pressure-time traces. The reason for the presence of pressure waves was found to be the non-uniform discharge of mass and energy of the combustion products from the vent holes of the flash tube.