A mathematical model of the bellows dispersion system is developed by combining the interior ballistic theory with structural dynamics theory to describe the deformation course of bellows.By analyzing the physical model of the bellows dispersion system,the dispersion course is divided into three stages.For each stage,mathematical model is built and its terminal conditions are given.The numerical simulation is based on the Runge-Kutta method and differential quadrature method.Simulation results of the model agree with those of the model built by only interior ballistics theory.However,this model is congruous with the actual dispersion course and can more easily determine the dispersion time and submunition displacement.