To study the reaction behavior of Al/PTFE (Aluminum/Polytetrafluoroethylene) cylindrical shells under inner explosive loading, this paper conducted explosive-driven experiments. The results showed that the flame duration of the reactive samples increased by 448.6% compared to the control group, and the peak overpressure increased by 40% compared to the control group. By comparing the differences between the flame images and overpressure–time curves of different samples, it was found that the anaerobic reaction occurring immediately after detonation significantly enhances the shock wave parameters, particularly the peak overpressure, while the subsequent aerobic reaction has a relatively minor effect on these parameters. To describe the enhancement of the shock wave parameters by the anaerobic reaction, a theoretical model was established from the perspective of shock wave coupling. In this model, the trailing shock wave generated by the Al/PTFE catches up and superimposes the leading shock wave generated by the explosive. During this process of catching up and superposition, the overpressure–time curve of the air shock wave transforms from a double-peak structure to a single-peak structure, and the peak overpressure is enhanced after such transformation. As the explosive mass increases, the air shock wave begins to be enhanced at a distance closer to the explosion center, and the duration of the double-peak structure decreases. Furthermore, as the propagation distance increases, the sample with the highest normalized enhancement rate shows a gradual decrease in the proportion of reactive material. These findings provide a valuable reference for the application of Al/PTFE shells combined with explosives.