The processes that take place within the Internal Ballistics cycle of an artillery round are highly influenced by geometric effects. They are also highly affected by the presence of a combination of energetic materials, such as the propellant, igniter, primer, and the combustible cartridge cases. For a more realistic simulation of these phenomena, a multidimensional and multicomponent numerical model is presented, based on adaptations and improvements of previous models of conservation equations, maintaining a two-phase, Eulerian–Eulerian approximation. A numerical method based on Finite Volumes and conservative flux schemes (Rusanov and AUSM+), with the ability to predict detonation effects, is proposed. As a result, a versatile 3D numerical code was obtained that was tested in the simulation of artillery firing with conventional and modular charges (MACS). Results show the code is able to characterize the heat and mass transfer of the different energetic materials during the combustion of the propellant and the cartridge cases, the gas expansion, and the projectile acceleration.