A study of the numerical modeling and prediction of nonlinear unsteady combustion instability within the combustion chamber of a solid rocket motor (SRM) is the main objective. The numerical model consists of a three-dimensional finite-element representation of a cylindrical-grain motor, coupled to a quasi-one-dimensional internal ballistic flow (IBF) model, where a quasi-steady rapid kinetic rate burning rate algorithm is used to model the propellant combustion and regression. Fluid-structure-combustion interaction subroutines are also employed to control the simulated motor firings and the data transferred between the fluid, structure and burning rate model components. Results illustrating the significant effects of structural vibrations on the burning rate and consequently the IBF are shown and compared to experimental data. Modeling considerations are illustrated, giving insight into the physical phenomena of SRM combustion instability.