This research is focused to investigate the cook-off response of a solid rocket motor (SRM) utilizing ammonium perchlorate/hydroxyl‑terminated polybutadiene (AP/HTPB) propellants under various heating environments, also assessing the damage degree of the motor casing and exploring the formation mechanism of ignition site. We have developed a three-dimensional (3-D) numerical model that encapsulates a range of response behaviors, including cook-off and mechanical destruction of the SRM. This model integrates multi-step thermal decomposition and combustion reaction models for the propellant, as well as a damage response model for the SRM. The response mechanisms of the SRM under varying thermal conditions have been simulated using a validated model. The study reveals that under both fast cook-off condition (FCC) and slow cook-off condition (SCC), the motors experienced deformation and rupture. Under FCC, ignition initiated at the motor head, reaching a maximum pressure of approximately 800 MPa near the ignition point. This led to the separation of the motor head from the main body, producing numerous casing fragments with the fragment cloud's radius showing a linear correlation to time (R = 0.73289t + 28.24286). The ignition delay was 224.5 s at an ignition temperature of 551.83 K. In contrast, under SCC, ignition occurred at the propellant's midsection inner surface, with a significantly lower maximum pressure of about 700 MPa. The motor expanded at this site, with the expansion radius exhibiting a nonlinear relationship to time (R = 0.19102t2 + 0.0096t + 32.97464). The casing then ruptured, causing extensive damage to both ends and generating a debris cloud with a radius that correlated linearly to time (R = 0.82147t + 26.70826). More severe longitudinal tearing, exceeding the FCC scenario, appeared in the motor body. The ignition delay time was 18.82 h. with an ignition temperature of 557.49 K.