Solid propellant is the highly energetic fuel burnt in the combustion chamber of ballistic weapons. It is manufactured, for this purpose, in either granular or stick form. Internal ballistics describes the behavior within the combustion chamber throughout the ballistic cycle upto projectile exit from the muzzle of the gun barrel. Over the last twenty years this has been achieved by modelling the process using two-phase flow equations. The solid granules or sticks constitute the first phase, which can be assumed to be incompressible over typical pressure ranges within the chamber. The gas-phase is composed of both the original ambient gas contained around the propellant and additional gas produced by the propellant gasifying on heating. Equations can be derived that describe the conservation of mass, momentum and energy in terms of average flow variables. The equations are a highly non-linear system of partial-differential- equations. High-speed flow features are observed in internal ballistics and ordinary fini te- difference methods are unsuitable numerical methods due to inaccurate prediction of discontinuous flow features. Modern shock-capturing methods are employed, which solve the system of equations in conservation form, with the ability to capture shocks and contact discontinuities. However, although the numerical solutions compare well with experiment over the bulk of the combustion chamber, the ignition models used in internal ballistics are unreliable. These are based on either gas or solid-surface temperature achieving some empirically measured 'ignition temperature' after which the propellant burns according to an empirical pressure dependent burning law. Observations indicate that this is not an adequate representation of ignition. Time differences between first solid gasification and ignition imply two distinct processes occurring. ]Further, ignition occurring in gas-only regions indicates that ignition is controlled by a gas-phase reaction. This thesis develops simple ideas to describe possible mechanisms for these physical observations. The aim is to provide an improved model of the ignition of solid propellant. A two stage reaction process is described involving endothermic gasification of the solid, to produce a source of reactant gas, followed by a very exothermic gas-phase ignition reaction. Firstly the gas-phase ignition is considered. A very simple reaction is suggested which is assumed to control the combustion of reactant gas, produced by solid gasification. Ignition is, by definition, the initiation of this exothermic reaction. Chemical kinetics are included in the gas-phase flow equations to explore the evolution of the reactant gas that is subject to changes in temperature and pressure. By assuming spatial uniformity, analytical solutions of the problem are deduced. The physical interpretation of the solution is discussed, in particular, the relationship between temperature, reactant concentration and ignition is explored. Numerical methods are required to solve the one-dimensional flow equations. Development of suitable CFD methods provides a method of solution. Finite-volume schemes, based on the original work by Godunov, are used to solve the conservation form of the equations. A simple test problem is considered whereby reactant gas is injected into a cylindrical combustion chamber. By examining the resulting flow histories, valuable information is gathered about the complicated coupling of chemistry and flow. Chemistry is included into a system of two-phase flow equations. By using standard averaging methods along with an equation for gas-phase species, equations are derived that describe the rate of change of average flo%v variables for both gas and particle phases. Numerical schemes are developed and some of the difficulties involved in two-phase flow systems, that are not an issue in single-phase flow, are presented. An internal ballistics application is considered as a test case and the solution discussed. The other important reaction involved in the combustion cycle, solid gasification, is explored. The model is based on detailed description of interphase mass and energy transfer at the solid-gas interface. This involves the solution of the heat conduction equation with a moving boundary that divides the solid and gas regions. Similar numerical schemes are constructed to solve the equations. Finally, this model is coupled with the equations of gas-phase reaction. This describes the complete cycle whereby increases in gas temperature cause the solid to increase in temperature and gasify. Subsequent gas-phase combustion of the reactant gases produces heat-transfer between the solid and gas and continues to accelerate gasification. Eventually this results in selfsustained combustion of the solid propellant.