Vortices generated in a solid rocket motor may cause pressure oscillations, which cause problems such as deteriorated flight performance and payload damage. The building-cube method (BCM) solver is expected to accurately predict such vortex flows using high-order schemes as well as easily manage complex configurations. The aim of this study is to establish an analysis method for the internal flow of a solid rocket motor using the BCM. Computational results obtained in this study are compared with analysis data based on other solvers as well as experimental data for validation. The BCM solver is applied to the validate the converging-diverging verification nozzle, upper jet model, and propellant surface ejection model. Furthermore, it effectively captures the three-dimensional (3D) trailing vortex downstream of the inhibitor and the propellant surface injection flow. In general, the 3D BCM solver accurately reproduces the internal flow field of the solid rocket motor.