We describe our numerical method for threedimensional simulations of solid rocket motors in which the internal gas dynamics, the combustion of the propellant, and the structural response are fully coupled. The combustion zone is treated as a thin layer using appropriate jump conditions, and the regression rate is determined using a nonlinear dynamic combustion model. An Arbitrary Lagrangian-Eulerian formulation is used in the gas dynamics and structural mechanics modules to follow the

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... of the propellant. We demonstrate the parallel scalability of our ALE implementation and its ability to handle significant burn back of the propellant on a model problem with a very high burn rate.