<p>An analytical model of condensed explosives under slow cook-off conditions was established based on the superposition principle and Sturm–Liouville method. The analytical model can quickly and accurately calculate the temperature distribution and ignition location under slow cook-off conditions. The analytical model enables deep probing of the physicochemical mechanisms and complex couplings underlying the thermal ignition of explosives. To validate the analytical model, a slow cook-off experiment was designed and conducted. The calculated normalized axial temperature distribution using the analytical model was compared with the experiment results. The two sets of data were consistent with each other. The finite difference method was used to compute the slow cook-off process and yielded a maximal error of 1% between analytical and numerical results. The comparison results verified the correctness of the model. The results of the analytical model indicate that the temperature increase due to the thermal decomposition of RDX accounted for only 0.2% of the overall temperature at ignition. The ignition locations are related to the length to diameter ratio of the charge. As the length-to-diameter (L/D) ratio of the charge increases, the ignition locations gradually move towards both ends. When L/D ≥ 5.22, the ignition locations are near the thermal boundary.</p>