The safety of missile under thermal condition should be evaluated for improving the reliability of the weapon. Aiming at the cook-off test for the research of the thermal stability of energetic materials, the calculating model was established. The heat transfer process and the quasi-static response of the cook-off bomb were simulated by means of thermodynamic coupling of LS-DYNA, an explicit finite element code. The ignition time, ignition temperature and the location of the ignition were determined. The thermal expansion of the cook-off bomb, the pressure distribution, the contours of the Von Mises effective stress and the effective stain were obtained. The result shows that the time consumed by ignition is deceasing with the increasing of the calefactive rate, while the temperature of the confinement is increasing with that. The pressure of the ignition location is also the high pressure location of the bomb. The maximum value of the effective stress and the effective stain are all in the cylindrical annular location of the explosive, where adjacent to the confinement.