The aim of this work is to present a novel numerical study applied to the chain propagation of the explosion of a special kind of propellant and the formation of overpressures inside a rigid and resistant partitioned vessel. A calculation methodology is developed to simulate the transmission of the explosion from one compartment to another adjacent compartment by the means of the hot flow through the shared orifice and finally to generalize this novel methodology for propellants to rigid and resistant complex multi-partitioned structures. The basic characteristics of the model have been developed for the ignition and the combustion of classical propulsive powders in a one-compartment vessel and adapted to a solid propellant such hexogen with appropriate parameters linked to simplified kinetics. A simple representation of the combustion phenomena based on energy transfers and the action of specific molecular species is presented. The model allows the study of various parameters such as the initial thermodynamic conditions, the location of the ignition energy, and the size of the inner openings or the vent areas. The model calculations have been compared with data obtained in the course of experimental works and indicate interesting preliminary trends.