Abstract: Granular materials are widely utilized in engineering applications, where their internal stress distribution and fracture behavior critically influence the stability and safety of structures such as rockfill dams and roadbeds. This study investigates the internal stress distribution and crack initiation mechanisms of spherical particles under uniaxial compression on the basis of two analytical solutions: the Hiramatsu-Oka (HO) solution and the Dean-Sneddon-Parsons (DSP) solution. The results indicate that the loading range significantly influences the internal stress distribution and crack initiation location. While the stress distributions obtained from both solutions are highly consistent, the DSP solution offers superior extensibility. Furthermore, this study extends the DSP solution to multi-point loading conditions and proposes a rapid evaluation framework for stress distribution and crack initiation in granular assemblies based on the scaled boundary finite element method (SBFEM)-DSP approach. This framework efficiently determines contact force distributions in granular assemblies using SBFEM and applies the stress superposition principle of the DSP solution to achieve a rapid assessment of stress fields and crack initiation regions. The findings provide a theoretical foundation for understanding the stress distribution and fracture mechanisms in granular materials and can be further applied to the rapid evaluation of deformation and potential breakage rates in granular assemblies.