In seismic calculations for buried pipes, the relationship between ground reaction forces and displacements acting in the axial direction of the pipe and perpendicular to the pipe axis is crucial. Ogata et al. conducted horizontal, vertical upward, and vertical downward load tests on small-diameter buried pipelines to evaluate the necessary soil spring characteristics for design purposes. Building upon this groundwork, we developed 3D analytical models to replicate and simulate pipeline behavior and subgrade reaction under similar loading scenarios. These 3D analytical models provide a comprehensive understanding of the subgrade reaction due to the pipe displacement and are powerful tools for optimizing design strategies and predicting structural performance. The integration of these models contributes significantly to enhancing the reliability and effectiveness of pipeline design and engineering practices in earthquake-prone areas.