A conjugated physical and mathematical model for the combustion of a composite solid propellant with addition of a polydisperse boron powder is presented. This model accounts for gas-dynamic processes in a two-phase, multi-rate, and multi-temperature heat-conducting medium, as well as heat transfer and reaction processes in solid propellant are taken into account above the surface of the solid propellant. Boundary conditions for the equality of heat and mass flows of propellant components are set on the propellant surface. The dependence of a burning rate of the composite solid propellant containing boron particles on the pressure above the propellant surface is derived from a numerical solution to the system of equations.