Solid rocket motors (SRMs) are widely used in space propulsion systems owing to their simplicity, reliability, and high thrust performance. This study focuses on the three-dimensional flow dynamics in SRMs equipped with inhibitors and nozzle cavities, which are critical components for controlling propellant combustion and optimizing thrust performance. Using the building-cube method, high-fidelity numerical simulations were conducted to analyze the internal flow field of a sub-scaled SRM model, including the effects of nozzle cavity geometry and volume on recirculation flow structures, velocity profiles, and vorticity distributions. The results revealed that the geometry and volume of the nozzle cavity significantly influenced the recirculation flow structures and their interactions with the nozzle head. Larger cavity volumes reduce the impact of recirculation flows on the nozzle head but introduce longitudinal recirculation flows, which contribute to flow field instability. The velocity and vorticity profiles show that cavity designs can mitigate flow instabilities near the nozzle head. However, excessive cavity volumes can lead to secondary flow phenomena. This study highlights the importance of three-dimensional flow analysis for understanding the complex interactions between inhibitors, nozzle cavities, and the surrounding flow field. The findings provide new insights for optimizing SRM design, particularly in reducing pressure oscillations and improving stability. Future studies should focus on unsteady flow phenomena using large-eddy simulations and experimental validation to further elucidate the mechanisms underlying flow-induced instabilities in SRMs.