To evaluate the structural integrity of a type of solid rocket motor grain with a largely increased area ratio using free-loading modified double-base grain, the Schapery integral nonlinear viscoelastic constitutive equation with damage is derived, and the numerical simulation model of solid rocket motor grain is constructed. According to the mission profile of the grain during the equipment period, the numerical simulation research on the mechanical response characteristics of the grain under three typical working conditions, namely, platform vibration, underwater explosion impact, and ignition pressurization during the launch is carried out. The simulation results show that under the three typical working conditions, the grain will not produce structural damage and defects, and the mechanical response of the grain under the platform vibration and explosion impact load is far less than that under the launch ignition pressurization. The ignition pressurization should be considered in the grain structural integrity design of this type or similar structure solid rocket motor.