The paper presents a lumped parameter mathematical model considering the changes of thermodynamic properties for combustion products of a composite propelling charge, and of a burning cartridge casing or shell as well, when shot with classic guns. In addition a method was proposed for considering not coincidental instants of ignition for particular components of the charge and also for powder grains of each component, and the heat flow into the walls containing the space with combustion products. Some results of numerical computations are shown for 125 mm 2A46 tank gun firing a hard core projectile. Moreover an evaluation of accuracy of the results is given on the basis of experimental data. Maximum pressure and muzzle velocity were basic criteria at the verification of the model. Analysis of accuracy for solutions of model equations allows a conclusion that the proposed mathematical model may be useful at the designing process of ammunition and guns.